Iron based high transition temperature superconductors

Xianhui Chen,1 Pengcheng Dai,2, 3 Donglai Feng,4 Tao Xiang,3, 5 and Fu-Chun Zhang6

1Department of Physics, University of Science and Technology of China, Hefei, China2Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA

3Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China4Department of Physics, Fudan University, Shanghai, China

5Collaborative Innovation Center of Quantum Matter, Beijing, China6Department of Physics, Zhejiang University, Hangzhou, China

In a superconductor electrons form pairs and electric transport becomes dissipation-less at lowtemperatures. Recently discovered iron based superconductors have the highest superconductingtransition temperature next to copper oxides. In this article, we review material aspects and physi-cal properties of iron based superconductors. We discuss the dependence of transition temperatureon the crystal structure, the interplay between antiferromagnetism and superconductivity by exam-ining neutron scattering experiments, and the electronic properties of these compounds obtainedby angle resolved photoemission spectroscopy in link with some results from scanning tunnelingmicroscopy/spectroscopy measurements. Possible microscopic model for this class of compounds isdiscussed from a strong coupling point of view.

INTRODUCTION

Superconductivity is a remarkable macroscopic quan-tum phenomenon, which was discovered by KamerlinghOnnes in 1911. As temperature decreases to below a criti-cal value, electric resistance of a superconductor vanishesand the magnetic field is repelled. Superconductors havemany applications. As an example, magnetic resonanceimaging has been widely used in medical facilities. Su-perconductors may be used to transport electricity with-out loss of energy. Conventional superconductivity iswell explained by Bardeen-Cooper-Schrieffer (BCS) the-ory, which was established in 1957. In a superconducting(SC) state, two electrons with opposite momenta attracteach other to form a bound pair. The pairing mechanismin a conventional superconductor is due to couplings be-tween electrons and phonons, which are quantum versionof lattice vibration. The transition temperatures (Tcs)are, however, very low, and usually well below 40 Kelvin(K). The low transition temperature has greatly limitedpractical applications of superconductors. It has beena dream to realize high Tc or room temperature super-conductors, which may revolutionally change the powertransmission in the world.

There was a great excitement after the discovery ofhigh Tc SC cuprate by Bednorz and Muller in 1986, whoreported Tc well above 30 K in La2−xCaxCuO4 [1]. Thesubsequent world-wide efforts in search of high Tc SCcuprate raised the transition temperature beyond the liq-uid nitrogen temperature of 77K for the first time [2]and the highest Tc at ambient pressure is 135K in Hg-based cuprates, which remains the record as of today. Allthe cuprates share a common structure element CuO2

plane, where Cu atoms form a square lattice. The sec-ond class of high Tc materials is iron based superconduc-tors, which was discovered by Hosono and co-workers inearly 2008 [3], who reported Tc = 26K in LaOFeAs with

part of O atoms replaced by F atoms. Soon after thisdiscovery, the transition temperature has been raised toabove 40K at ambient pressure by substitution of differ-ent elements [4–7]. The highest Tc in bulk iron-basedsuperconductors is 55K in SmO1−xFxFeAs reported byRen et al. [6], and similarly in Gd1−xThxFeAsO [8].So far many families of iron-based superconductors havebeen discovered [9–13]. Most recently, monolayer FeSesuperconductivity on top of substrate SrTiO3 has beenreported [14], and there is an indication that Tc is likelyhigher than the bulk ones.

Study of iron based superconductors and their phys-ical properties have been one of the major activities incondensed matter physics in the past several years. Atthe time when the iron based superconductor was discov-ered, scientists in the field of superconductivity were wellprepared. Several powerful new techniques such as angleresolved photoemission spectroscope (ARPES), scanningtunneling microscopy (STM), have been well developedduring the course of studying high Tc cuprates. Thesetechniques together with some more conventional tech-niques such as neutron scattering, nuclear magnetic res-onance (NMR), optical conducting measurements, havebeen applied to examine the properties of the new com-pounds. Iron based superconductivity shares many com-mon features with the high Tc cuprates. Both of themare unconventional superconductors in the sense thatphonons unlikely play any dominant role in their super-conductivity. Both are quasi-two dimensional, and theirsuperconductivity is in the proximity of antiferromag-netism. On the other hand, iron based superconductorshave a number of distinct properties from the cuprates.The parent compounds of the SC cuprates are antiferro-magnetic (AF) Mott insulators due to strong Coulomb re-pulsion, and the lightly doped superconductors are dopedMott insulators [15–18]. On the other hand, the par-ent compounds of iron based superconductors are semi-

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metallic. Dynamic mean field calculations indicate thatthe iron based compounds are close to metal-insulatortransition line but are at the metallic side [19]. In thecurpates, the low energy physics is described by a singleband [20], while in the iron-based compounds, there aremulti orbitals involved. Despite over 25 years of study,some of the physics in the cuprates remain controversial.The investigation of iron based superconductors may helpus to understand the unconventional superconductivityand also provide a new route for searching higher tem-perature superconductors.

The purpose of this article is to provide an overall pic-ture of the iron based superconductivity based on ourpresent understanding. Instead of giving a broad reviewto cover all the experimental and theoretical develop-ments in this field, we will discuss basic physical prop-erties of the materials and the underlying physics by ex-amining limited experiments and theories. We refer thereaders to several recent review papers [21–27] for morecomplete description of the field. The rest of the articleis organized as follows. In section 2, we discuss materialsaspect of the compounds. Antiferromagnetism and su-perconductivity will be discussed in section 3. In section4, we discuss electronic structure of iron-based materi-als largely based on ARPES and STM experiments. Webriefly present our theoretical understanding of the elec-tronic structure and superconductivity in section 5. Thearticle will end with a summary and perspective in sec-tion 6.

MATERIALS AND CRYSTAL STRUCTURES

Material classification and crystal structures

Substitution of magnetic Sm for non-magnetic La leadsto a dramatic increase in Tc from 26 K in LaFeAsO1−xFxto 43 K in SmFeAsO1−xFx [3, 4]. This suggests thata higher Tc is possibly realized in the layered oxypnic-tides. The achieved Tc of 43 K in SmFeAsO1−xFx ishigher than the commonly believed the upper limit (40K) of electron-phonon mediated superconductors, whichgives compelling evidences for classifying layered iron-based superconductors as a family of unconventional su-perconductors. Subsequently, many new iron-based su-perconductors with diverse crystal structures were foundand they can be categorized into several families accord-ing to their structural features.

The iron-based superconductors share the commonFe2X2 (X=As and Se) layered structure unit, which pos-sesses an anti-PbO-type (anti-litharge-type) atom ar-rangement. The Fe2X2 layers consist of edge-sharedFeX4/4 tetradedra, which has 4m2 site symmetry. Inthe Fe2X2 layers, X ions form a distorted tetrahedral ar-rangement around the Fe ions, giving rise to two distinctX-Fe-X bond angles with multiplicities of two and fourwhich we refer to as α and β, respectively.

FeSe (Tc = 8 K) has the simplest structure amongthe known iron-based superconductors, which is called11 phase [11]. FeSe is formed by alternate stacking ofthe anti-PbO FeSe layers. In FeSe, the cations and an-ions occupy the opposite sites to Pb and O atoms oflitharge, so that we call it anti-PbO or anti-litharge struc-ture. FeSe adopts a space group of P4/nmm. TheFe2Se2 monolayer consists of flat Fe2 square-net sand-wiched by two Se monolayers. Consequently, each Featom is coordinated with four Se atoms to establish theedge-shared FeSe4 tetrahedron, forming a 2D square-netFe2Se2 monolayer. As shown in Fig. 1, these tetrahedralFe2X2 layers can be separated by alkali and alkali-earthcations, LnO layers or perovskite-related oxydic slabs.Fig. 1 also illustrates the crystal structures of AFeAs,AeFe2As2, LnOFeAs. Their basic crystallographic dataare listed in Table I. The simplest FeAs-based supercon-ductor in structure is the AFeAs (A = Li and Na, called111 phase) [12, 13, 28]. AFeAs crystallizes in an anti-PbFCl-type structure, which adopts a Cu2Sb (or Fe2As)structure. AFeAs has the space group of P4/nmm andeach unit cell includes two chemical formula, that is 2A,2Fe and 2As. Fe and As are arranged in anti-PbO-typelayers with double Li/Na planes located between the lay-ers in square-based pyramidal coordination by As.

With additional atoms added into the anti-PbFCl-typestructure, we can achieve ZrCuSiAs-type 1111 supercon-ductors. Up to now, the highest Tc ∼ 55 K in iron-based superconductors has been achieved in fluorine-

3

c

b

a

FeSe/As

Li/NaAe

Ln

O

AeOMO2

Ae

11

FeSe111

AFeAs

122

AeFe2As2

1111

LnOFeAs (Aen+1Mn

Oy)Fe2As2 (Aen+2Mn

Oy)Fe2As2

FIG. 1. The schematic view of the crystal structures for several typical types of iron-based superconductors, in which A, Ae,Ln and M stand for alkali, alkali earth, lanthanide, and transition metal atoms.

doped or oxygen-deficient LnFeAsO compounds (Ln rep-resents rare-earth metal atoms) [6], which are usuallybriefly written as 1111 phase. LnFeAsO compoundshave a tetragonal layered structure at room tempera-ture, with space group P4/nmm. The schematic viewof their crystal structure is shown in Fig. 1. The ear-liest discovered 1111 compound with relative high Tc isLaFeAsO [3], with lattice constants at room temperaturea = 4.03268(1) A, c = 8.74111(4) A. For these 1111 com-pounds, their structure consists of alternate stacking ofFeAs layers and fluorite-type LnO layers. For LaFeAsO,the distance between the adjacent FeAs and LaO layersis 1.8 A. The lattice constants a and c decrease withreducing the ion radii of the rare-earth metals. Withthe decreasing radii of the rare-earth metal ions, the op-timal Tc first increases rapidly, reaching the highest Tc(= 55 K) in the doped SmFeAsO system [6, 29], andthen decreases slightly with further reducing the radii ofthe rare-earth metal ions. Besides LnFeAsO systems,there are other types of 1111 FeAs-based compound,AeFFeAs (Ae = Ca, Sr and Ba) [30, 31] and CaHFeAs[32]. AeFFeAs (Ae =Ca, Sr and Ba) and CaHFeAs arealso parent compounds of superconductors [33–35]. Veryrecently, a new 1111-type FeSe-derived superconductor,LiFeO2Fe2Se2 with Tc ≈ 43 K, was synthesized by Lu etal [36].

The other typical type of compounds, ThCr2Si2-typeiron arsenides, possess only single layers of separat-ing spacer atoms between Fe2X2 (so called 122 struc-ture), which is adopted by AeFe2As2 (Ae = Ca, Sr,Ba, Eu, K etc.) [10, 37–39] and AxFe2−ySe2 (A=K,Rb, Cs, Tl/K and Tl/Rb) [40–43]. AeFe2As2 adoptsbody-centered tetragonal lattice and has space group of

I4/mmm. In FeAs-122, the highest Tc ∼ 49 K can beachieved in Pr-doped CaFe2As2 [44]. However, some re-cent reports revealed that such superconductivity withTc higher than 40 K should be ascribed to a new struc-tural phase (Ca,Ln)FeAs2 (Ln = La, Pr). Crystal struc-ture of (Ca,Ln)FeAs2 is derived from CaFe2As2, withshifting the adjacent FeAs layers along the 45◦ directionof ab-plane by half lattice length on the basis of CaFe2As2and then intercalating one additional As-plane and oneCa-plane for every two CaFeAs blocks [45]. FeSe-derivedsuperconductors AxFe2−ySe2 also crystallize in 122 struc-ture, which have a Tc of ∼ 30 K in crystals grown bythe high-temperature melting method [40–43] or higherthan 40 K by co-intercalation of alkali atoms and cer-tain molecules (NH3 or organic) by a low-temperaturesolution route [46–49].

According to the previous knowledge in the high-Tc cuprates, superconductivity is closely related to theseparating spacers between adjacent conducting lay-ers. Therefore, compounds with complicated struc-tures between FeAs layers were synthesized. Up tonow, Aen+1MnOyFe2As2 and Aen+2MnOyFe2As2 (Ae= Ca, Sr, Ba; M = Sc, V, (Ti,Al), (Ti,Mg) and(Sc,Mg)) systems have been successfully synthesized,where y∼3n-1 for the former and y∼3n for the latter[50–53]. Fig. 1 show the crystal structures for thecase of n=1. They all adopt tetragonal lattice. AllAen+1MnOyFe2As2 compounds share the same spacegroup of D174

h -I4/mmm, while for Aen+2MnOyFe2As2,its space group is P4/nmm for n = 2 and 4, whereasP4mm for n = 3. For Aen+1MnOyFe2As2, n per-ovkite layers are sandwiched between adjacent FeAslayers, while for Aen+2MnOyFe2As2 there are n per-

4

TABLE I. Maximum temperatures of the SC transition un-der ambient pressure and lattice parameters of undoped com-pounds for some typical iron-pnictides.

Compound Maximum Tc(K) Space group a (A) c (A) Ref.

LiFeAs 18 P4/nmm 3.775 6.353 [4]

BaFe2As2 38 I4/mmm 3.963 13.017 [13]

LaOFeAs 41 P4/nmm 4.035 8.740 [24]

CeOFeAs 41 P4/nmm 3.996 8.648 [24]

PrOFeAs 52 P4/nmm 3.926 8.595 [24]

NdOFeAs 51.9 P4/nmm 3.940 8.496 [24]

SmOFeAs 55 P4/nmm 3.940 8.496 [24]

GdOFeAs 53.5 P4/nmm 3.915 8.435 [24]

TbOFeAs 48.5 P4/nmm 3.898 8.404 [24]

ovkite layers plus one rock-salt layer in each blockinglayer. The Aen+2MnOyFe2As2 and Aen+2MnOyFe2As2can be SC with Tc ranging from 17 to 47 K [52–54]. There are some other FeAs-based superconduc-tors with quite complicated structures, such as Ca-Fe-Pt-As system Ca10(Pt3As8)(Fe2As2)5 (so called 10-3-8),Ca10(Pt4As8)(Fe2As2)5 (so called 10-4-8) [55, 56] andBa2Ti2Fe2As4O [57] and so on.

There is a resistivity anomaly in the parent compoundof LaFeAsO at around 150 K, which disappears as super-conductivity emerges [3]. It was clarified later by de laCurz et al. through neutron scattering experiment thatsuch an anomaly around 155 K could be attributed tothe structural phase transition [58]. As shown in Fig. 2,a structural transition occurs around 155 K in undopedLaOFeAs. The space group of the low-temperature struc-ture was clarified to be the orthorhombic Cmma [59, 60].The space group changes from the high-temperaturetetragonal P4/nmm to low-temperature orthorhombicCmma, corresponding to a transformation from 5.70307A×5.70307 A square network (for comparison, here weuse a

√2, so that space group becomes F4/mmm) to

5.68262 A×5.571043A with a slight shrink of the c-axislattice constant, as shown in the left panel of Fig. 2 [61].In the structural transition, chemical formulae in eachunit cell change from 2 to 4 with a symmetry degradation.With decreasing temperature, the parent and slightlydoped AeFe2As2 (Ae = Ca, Sr, Ba, and Eu) also undergoa structural transition from high-temperature tetragonalphase to low-temperature orthorhombic phase. The low-temperature orthorhombic phase has the space group ofFmmm [10, 62]. Fig. 3 shows that FeAs4 tetrahedron dis-torts in the structural transition in BaFe2As2. The As-Fe-As angles around 108.7◦ become nonequivalent andevolve to two values of 108.1◦ and 108.7◦ respectively[10]. Such a structural transition from high-temperaturetetragonal symmetry to low-temperature orthorhombicsymmetry occurs among the undoped and underdopedFeAs-based 111, 122 and 1111 phases.

Relation between crystal structure andsuperconductivity

By summarizing plenty of data about crystal structureand Tc for iron-based superconductors, it is found that Tcis related to structure parameters [63–65]. In particular,there is a close relation between the anion (As, P, Se, andTe) height from the Fe layer (h) and Tc, as shown in Fig.4a [63]. h depends on the type of anion, increasing in turnfrom FeP, FeAs, FeSe to FeTe. Due to the relative small hin FeP based superconductors, their Tcs are usually lowerthan those in FeAs-based superconductors. For example,in La-1111 phase, as P is substituted by As, Tc is en-hanced dramatically from 7 to 26 K, due to the increase ofh. For FeAs-based 1111 phase, as the substitutions of Laby Nd and Sm increases h to around 1.38 A, Tc increasesdramatically from 26 to 56 K. After crossing this max-imum, the Tc of TbFeAsO0.7, Ba0.6K0.4Fe2As2, NaFeAsor LiFeAs decreases with increasing h. The data of op-timally doped FeSe1−xTex, FeSe0.57Te0.43, seem to alsofollow the same curve. As a result, such a dependence ofTc on h seems to be universal for 1111, 122, 111 and 11iron-based superconductors. Though the maximum Tcof the superconductors with thick blocking layer remainsunconfirmed, the data of the 42622 superconductor obeythe same universal curve, except for a small deviation,which may suggest that the enhancement of 2D charac-ter could induce a Tc higher than 56 K. Note that for sucha universal correspondance between h and Tc, there is anexception in FeSe-derived superconductors. As shown inFig. 4b, for the FeSe-derived materials, a minimum of Tccan be observed at h ≈ 1.45 A[36], instead of a maximumas shown in Fig. 4a. This may suggest some new under-lying physics in FeSe-derived superconductors comparedto FeAs-based ones. The bond angle of As-Fe-As, whichreflects the distortion of the FeAs4 tetrahedron, was alsothought to be closely related to superconductivity [66].As shown in the Fig. 4c, the maximum Tc was achievedwhen the FeAs4 tetrahedron is in perfectly regular, withthe bond angle of 109.47◦.

5

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130 140 150 160 170 180

T (K)

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(–2, 2, 0)M

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FIG. 2. (a) Neutron scattering result on structural transitions on LaOFeAs [58]. (b) The temperature dependence of latticeconstants for different F doping levels in SmFeAsO1−xFx system.

FIG. 3. As-Fe-As bond angles of BaFe2As2 at high and lowtemperature respectively (data from Ref. [10]).

THE INTERPLAY BETWEEN MAGNETISMAND SUPERCONDUCTIVITY

Soon after the discovery of iron pnictide superconduc-tor LaFeAsO1−xFx with Tc = 26 K [3], band calcula-tions based on transport and optical conductivity mea-surements predicted the presence of a collinear AF [orspin-density-wave (SDW)] state in the parent compounds[67], which was subsequently confirmed by neutron scat-tering experiments as shown in the inset of Fig. 5 [58].The same collinear AF state was later found in the parentcompounds of most iron pnictide superconductors [62].Although the electronic phase diagrams for different fam-ilies of iron-based superconductors can be somewhat dif-ferent [21], they all share the common feature of an AFordered parent compound [68]. This has inspired many to

believe that the magnetic excitations play an importantrole in the mechanism of the high-Tc superconductivityin iron-based supercondutors [69]. To test if this is in-deed the case, systematic investigation on the magneticorder and spin excitations through out the phase dia-gram of different families of iron-based superconductorsis essential. Figure 5 shows the electronic phase diagramof electron and hole-doped BaFe2As2 iron pnictides de-termined from transport and neutron scattering exper-iments [24, 70–77]. For electron-doped BaFe2−xNixAs2,the maximum Tc = 20 K is around x ≈ 0.1 and supercon-ductivity ceases to exist for x ≥ 0.25 [78]. For hole-dopedBa1−xKxFe2As2, superconductivity exists in the entirephase diagram with maximum Tc = 38 K near x ≈ 0.33and Tc = 2 K for pure KFe2As2 [79]. The arrows inthe figure indicate iron pnictides where spin excitationsin the entire Brillouin zone have been mapped out byinelastic neutron scattering (INS) experiments [80–86].

Effect of electron-doping to spin waves of ironpnictides

We first discuss the electron-doping evolution of spinexcitations in BaFe2−xNixAs2. With the development ofneutron time-of-flight spectroscopy, the entire spin wavespectra were obtained in CaFe2As2 [87] and BaFe2As2[80] soon after the availability of single crystals of thesematerials. The solid lines in Figure 5b show the disper-sion of spin waves in BaFe2As2 along the [1,K] and [H, 0]directions in reciprocal space, where the collinear AF or-der occurs at the QAF = (1, 0) wave vector position [80].

6

a b c

FIG. 4. (a) Anion height dependence of Tc in iron-based superconductors [63]. (b) Anion height dependence of Tc in FeSe-derived superconductors.[36] (c) The relation between the As(top)-Fe-As(top) angle a and Tc of iron-based superconductors[64].

Upon electron-doping to induce optimal superconduc-tivity, spin excitations become broader at low-energies(E ≤ 80 meV) while remain unchanged at high ener-gies (E > 80 meV) [81]. The low-energy spin excitationscouple to superconductivity via a collective spin excita-tion mode termed neutron spin resonance [88–91], seenalso in copper oxide superconductors [92]. The red circleand yellow upper triangle symbols in Fig. 5b show spinexcitation dispersions of the optimally electron dopedBaFe1.9Ni0.1As2 at T = 5 K and 150 K, respectively[81]. With further electron-doping, superconductivity issuppressed for x ≥ 0.25 [78], Figure 5c shows the dis-persions of spin excitations of BaFe1.7Ni0.3As2 comparedwith that of the undoped BaFe2As2 [80, 83]. A large spingap forms for energies below ∼50 meV as shown in thedashed line region. The dispersions of spin excitationsare also softer than that of BaFe2As2 [80, 83]. Figures 5dand 5e show the dispersions of spin excitations for opti-mally hole-doped Ba0.67K0.33Fe2As2 and hole over-dopedKFe2As2, respectively. The solid lines are the spin wavedispersions of BaFe2As2 [80, 83].

Figure 6 summarizes the evolution of the two-dimensional constant-energy images of spin excitationsin the (H,K) plane at different energies as a func-tion of electron-doping from the undoped AF parentcompound BaFe2As2 to overdoped nonsuperconductingBaFe1.7Ni0.3As2 [75, 80, 83]. In the undoped case, thereis an anisotropy spin gap below ∼15 meV so there areessentially no signal at E = 9± 3 meV (Fig. 6a). Uponelectron-doping to suppress static AF order and inducenear optimal superconductivity with x = xe = 0.096,the spin gap is suppressed and low-energy spin excita-tions are dominated by a resonance that couples withsuperconductivity (Fig. 6f) [75, 89–91]. Moving to elec-tron overdoped side with reduced superconductivity inBaFe2−xNixAs2 with x = 0.15 (Tc = 14 K) and 0.18(Tc = 8 K), spin excitations at E = 8 ± 1 meV be-

come weaker and more transversely elongated (Figs. 6kand 6p) [75]. Finally on increasing electron doping levelto x = 0.3 with no superconductivity, a large spin gapforms in the low-energy excitations spectra (Fig. 6u).Figures 6b-6e, 6g-6j, 6i-6o, 6q-6t,6v-y show spin ex-citations at different energies for BaFe2−xNixAs2 withx = 0, 0.096, 0.15, 0.18, and 0.30, respectively. While spinexcitations at energies below E = 96 ± 10 meV changerather dramatically with increasing electron-doping, highenergy spin excitations remain similar and only softenslightly.

The effect of hole-doping to the spin excitations ofiron pnictides

Figure 7 shows the evolution of spin excitations inthe similar two-dimensional constant-energy images asa function of hole-doping. For pure KFe2As2, incom-mensurate spin excitations along the longitudinal direc-tion are seen at E = 8 ± 3 (Fig. 7a) and 13 ± 3 (Fig.7b) [86]. Upon further increasing energy, no clear mag-netic scattering can be seen (Fig. 7c). For optimallyhole-doped Ba0.67K0.33Fe2As2, the low-energy spin ex-citations change from transversely elongated ellipses asshown in Fig. 6f to longitudinally elongated ellipse atE = 5±1 meV (Fig. 7d). On increasing the energy to theneutron spin resonance energy of E = 15 ± 1 meV, spinexcitations become isotropic in reciprocal space (Fig. 7e).Spin excitations become transversely elongated again forenergies above E = 50 ± 2 meV (Figs. 7f-7i), very simi-lar to spin excitations in electron-doped BaFe2−xNixAs2(Fig. 6). From data presented in Figs. 6 and 7, onecan establish the basic trend in the evolution of spinexcitations via electron and hole doping to the parentcompound BaFe2As2. While electron-doping appearsto mostly modify the low-energy spin excitations and

7

Doping Concentration (x)0 0.1 0.30.20.250.50.751.0

40

80

120

160T

(K

)BaFe2-x

NixAs2Ba1-x

KxFe2As2

SC

AFM

PM

AFM

PM

SC

(1,0)

IC-SF

H

KC-SF

H

K

(1,0)

Fe2+

bo

ao

IC-AFM

0.3

xh = 0.33xh = 1.0

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J1a

J1b

xe = 0.1

C-SF

H

K

(1,0)

0.150.18

0.0

[1, K ] (r.l.u.)

1.0 0.5 0.5 1.0

1.001.00 0.50 1.25 1.500

200

100

1.00.6 0.8 1.2 1.40

20

xe = 0.3

x = 0

xh = 0.33

x = 0 x = 0

xh = 1

150 K

5 K

1.00

[1, K ] (r.l.u.)

-1.00 -0.50 1.25 1.50

E (

me

V)

200

100

0

[H, 0] (r.l.u.)

200

100

0

xe = 0.1

x = 0

E (

me

V)

[H, 0] (r.l.u.)[1, K ] (r.l.u.) [H, 0] (r.l.u.)

a

b c

d e

FIG. 5. (a) The electronic phase diagram of electron andhole-doped BaFe2As2, where the arrows indicate the dop-ing levels of inelastic neutron scattering experiments. Theright inset shows crystal and AF spin structures of BaFe2As2with marked the nearest (J1a, J1b) and next nearest neighbor(J2) magnetic exchange couplings. The inset above xe = 0.1shows the transversely elongated ellipse representing the low-energy spin excitations in electron-doped BaFe2−xNixAs2 inthe (H,K) plane of the reciprocal space. The left insetsshow the evolution of low-energy spin excitations in hole-doped Ba1−xKxFe2As2 in the (H,K) plane. C-SF and IC-SF indicate commensurate and incommensurate spin fluctu-ations, respectively. (b-e) The solid lines in the figure arespin wave dispersions of the undoped BaFe2As2 along the twohigh-symmetry directions. The symbols in (b), (c), (d), and(e) are dispersions of spin excitations for BaFe1.9Ni0.1As2,BaFe1.7Ni0.3As2, Ba0.67K0.33Fe2As2, and KFe2As2, respec-tively [83]. The shaded areas indicate vanishing spin exci-tations.

make them more transversely elongated with increas-ing electron counts, high-energy spin excitations do notchange dramatically. Therefore, the Fermi surface mod-ifications due to electron doping affect mostly the low-energy spin excitations, suggesting that they are aris-ing from itinerant electrons. The high-energy spin ex-citations weakly dependent on electron-doping inducedFermi surface changes are most likely arising from local-ized moment. The lineshape change from transversely tolongitudinally elongated ellipse in low-energy spin exci-

tations of iron pnictides upon hole-doping is consistentwith the random phase approximation calculation of thedoping dependence of the nested hole and electron Fermisurfaces [84, 93]. The absence of dramatic changes inhigh-energy spin excitations again suggests the presenceof local moments independent of Fermi surface changesinduced by electron or hole-doping. Comparing with res-onant inelastic X-ray scattering (RIXS) results on hole-doped Ba0.6K0.4Fe2As2 [94], we note that dispersion de-termined from RIXS is consistent with neutron scatteringwhile the intensity is lower. At present, it is unclear howto understand the intensity of the RIXS measurements.

Evolution of local dynamic susceptibility as afunction of electron and hole-doping

To quantitatively determine the electron and hole-doping evolution of the spin excitations in iron pnictides,one can estimate the energy dependence of the local dy-namic susceptibility per formula unit, defined as χ′′(ω) =∫χ′′(q, ω)dq/

∫dq, where χ′′(q, ω) = (1/3)tr(χ′′αβ(q, ω))

[81, 95]. The dashed squares in Figs. 6 and 7 show theintegration region of the local dynamic susceptibility inreciprocal space. Figure 8a and 8b summarizes the en-ergy dependence of the local dynamic susceptibility forhole (Ba1−xh

KxhFe2As2 with xh = 0, 0.33, 1) and elec-

tron (BaFe2−xeNixeAs2 with xe = 0, 0.096, 0.15, 0.18, 0.3)doped iron pnictides. From Figure 8a, we see that theeffect of hole-doping near optimal superconductivity isto suppress high-energy spin excitations and transferspectral weight to lower-energies. The intensity changesacross Tc for hole-doped Ba0.67K0.33Fe2As2 are muchlarger than that of the electron-doped BaFe1.9Ni0.1As2[81]. As a function of increasing electron-doping, thelocal dynamic susceptibility at low-energies decreasesand finally vanishes for electron-overdoped nonsupercon-ducting BaFe1.7Ni0.3As2 with no hole-like Fermi surface[75, 83]. This again confirms the notion that supercon-ductivity in iron pnictide is associated with itinerant elec-tron and low-energy spin excitation coupling between thenested hole and electron Fermi surfaces [83].

Correlation between spin excitations andsuperconductivity

In conventional BCS superconductors [96], supercon-ductivity occurs via electron-lattice coupling below Tc.The SC condensation energy Ec (= −N(0)∆2/2 and∆ ≈ 2~ωDe

−1/N(0)V0 , where N(0) is the electron densityof states at zero temperature) and Tc are controlled bythe strength of the Debye energy ~ωD and electron-latticecoupling V0 [96–98]. For unconventional superconduc-tors derived from electron and hole-doping to their AFordered parent compounds, short-range spin excitations

8

H (r.l.u.)

K (

r.l.

u.)

0

1.5

-1.5

a

H (r.l.u.)

K (

r.l.

u.)

f

b

c

g

h

x = 0.0

60±10 meV 60±10 meV

H (r.l.u.)

K (

r.l.

u.)

0

2

-2

H (r.l.u.)0 2-2

K (

r.l.

u.)

0 2-2

0

-2

2

d

e

i

j

96±10 meV

181±10 meV

+

96±10 meV

0 1.5-1.5 0 1.5-1.5

xe = 0.30

0

1.5

-1.5

181±10 meV

0

5

19±5 meV19±5 meV

0

16

H (r.l.u.)

0

1.5

-1.5

H (r.l.u.) H (r.l.u.)

k p

l

m

q

r

xe = 0.096

8±1 meV 8±1 meV 8±1 meV

16±2 meV 16±2 meV

60±10 meV60±10 meV

+

+

S(Q

,ω)

(mb

r sr

m

eV

f

.u.

)-1

-1-1

0

4

16±2 meV

0

4

60±10 meV

H (r.l.u.) H (r.l.u.) H (r.l.u.)0 2-2 0 2-20 2-2

n

o

s

t

96±10 meV 96±10 meV

181±10 meV

+

0

1.2

96±10 meV

0

0.8

xe = 0.15 x

e = 0.18

181±10 meV 181±10 meV

9±3 meV

+0

1.5

-1.5

9±3 meV

0 1.5-1.5 0 1.5-1.5 0 1.5-1.5

K (

r.l.

u.)

u

v

w

x

y

FIG. 6. Constant-energy slices through magnetic excitations of electron-doped iron pnictides at different energies. The colorbars represent the vanadium normalized absolute spin excitation intensity in the units of mbarn sr−1meV−1f.u.−1. (a-e) Spinwaves of BaFe2As2 at excitation energies of E = 9±3, 19±5, 60±10, 96±10, and 180±10 meV [80]. Spin waves peak at the AFordering wave vectors QAF = (±1, 0) in the orthorhombic notation. Spin waves are also seen at QAF ≈ (0,±1) due to the twindomains of the orthorhombic structure. (f-j) Two-dimensional images of spin excitations for BaFe1.904Ni0.096As2 at E = 8± 1,16±2, 60±10, 96±10, 181±10 meV. Identical slices as that of (f-j) for (k-o) BaFe1.85Ni0.15As2 and (p-t) BaFe1.82Ni0.18As2 [75].(u-y) Constant-energy slices through magnetic excitations of electron overdoped doped nonsuperconducting BaFe1.7Ni0.3As2at E = 9± 3, 19± 5, 60± 10, 96± 10, 181± 10 meV [83].

may mediate electron pairing for superconductivity [69].Here the SC condensation energy should be accounted forby the change in magnetic exchange energy between thenormal (N) and superconducting (S) phases at zero tem-perature via ∆Eex(T ) = 2J [〈Si+x · Si〉N − 〈Si+x · Si〉S],where J is the nearest neighbor magnetic exchange cou-pling, 〈Si+x · Si〉 is the dynamic spin susceptibility inabsolute units at temperature T , and S(Q, E = ~ω) isrelated to the imaginary part of the dynamic suscepti-bility χ′′(Q, ω) via S(Q, ω) = [1 +n(ω, T )]χ′′(Q, ω) with[1 + n(ω, T )] being the Bose population factor [69].

Since the dominant magnetic exchange couplings areisotropic nearest neighbor exchanges for copper oxide su-perconductors [99, 100], the magnetic exchange energy∆Eex(T ) can be directly estimated using the formulathrough carefully measuring of J and the dynamic spinsusceptibility in absolute units between the normal andSC states [101–103]. For heavy Fermion [104] and ironpnictide superconductors [83], one has to modify the for-mula to include both the nearest neighbor and next near-est neighbor magnetic exchange couplings. The calcula-tions of the magnetic exchange energies in CeCu2Si2 [104]and optimally hole-doped Ba0.67K0.33Fe2As2 [83] revealthat they are large enough to account for the SC conden-

sation energy, thus suggesting that spin excitations couldbe the driving force for mediating electron pairing for su-perconductivity. These results are consistent with NMRexperiments [105], where the presence low-energy spinexcitations is found to be associated with Fermi surfacenesting and the absence of nesting in electron overdopediron pnictides supresses the low-energy spin excitations.These results are also consistent with the absence of spinexcitations in non-superconducting collapsed tetragonalphase of CaFe2As2 from inelastic neutron scattering mea-surements [106].

9

H (r.l.u.)

0

1

-1

K (

r.l.

u.)

K (

r.l.

u.)

0

1

-1

a

H (r.l.u.) H (r.l.u.)

-2

3

1 20

K (

r.l.

u.)

0 2-2

0

-11 20

1

-2

7

-0.3

0.7

-2

3

-0.5

2.5

-2

5

-0.3

0.8

d g

b

c

e

f

h

i

xh

= 1.0

8±3 meV 5±1 meV 115±10 meV

13±3 meV 15±1 meV

50±2 meV53±8 meV

+

+

+

+

+

S(Q

,ω)

(mb

r sr

m

eV

f

.u.

)-1

-1-1

-0.3

0.7

155±10 meV

-0.2

0.4

195±10 meV

0

2

-2

0

2

-2

0

2

-2

0

1

-1

0

1

-1

0

-1

1

xh

= 0.33 xh

= 0.33

FIG. 7. Two-dimensional images of spin excitations at different energies for hole-doped KFe2As2 at 5 K. (a) E = 8± 3 meVobtained with Ei = 20 meV along the c-axis. The right side incommensurate peak is obscured by background scattering. (b)13±3 with Ei = 35 meV, and (c) 53±8 meV with Ei = 80 meV. For Ba0.67K0.33Fe2As2 at T = 45 K, images of spin excitationsat (d) E = 5 ± 1 meV obtained with Ei = 20 meV, (e) 15 ± 1 meV with Ei = 35 meV, and (f) 50 ± 2 meV obtained withEi = 80 meV. Spin excitations of Ba0.67K0.33Fe2As2 at energy transfers (g) 115± 10 meV; (h) 155± 10 meV (i) 195± 10 meVobtained with Ei = 450 meV, all at 9 K. Wave vector dependent backgrounds have been subtracted from the images [83].

10

20

30

40

χ”(

ω)

(μB

2 e

V-1

f.u

.-1)

0

0 100 200 300

E (meV)

xe = 0.096, 5 K

xe = 0.30, 5 K

xe = 0.15, 5 Kxe = 0.18, 5 K

10

20

30

40

χ”(

ω)

(μB

2 e

V-1

f.u

.-1)

0

0 100 200 300

E (meV)

a

b

x = 0.0, 7 K

xh = 0.33, 5 K

xh = 1.0, 5 K

x = 0.0, 7 K

xh = 0.33, 45 K

FIG. 8. Energy and temperature dependence ofthe local dynamic susceptibility χ′′(ω) for (a) BaFe2As2,Ba0.67K0.33Fe2As2, KFe2As2, and (b) BaFe2−xeNixeAs2 withxe = 0, 0.096, 0.15, 0.18, 0.3. The intensity is in absolute unitof µ2

BeV−1f.u.−1 obtained by integrating the χ′′(Q,ω) in thedashed regions specified in Figs. 6 and 7.

ELECTRONIC PROPERTIES

Electronic properties of the iron based superconductoris critical for understanding its phase diagram, mecha-nism and transport behaviors. In this section, we focus

on the electronic properties of these compounds obtainedby ARPES, in link with some results from scanning tun-neling microscopy/spectroscopy (STM/STS) measure-ments. We note that more detailed reviews of the ARPESresults can be found in Refs. 211 and 212.

The electronic structure of the iron based supercon-ductors and related materials is characterized by themulti-band and multi-orbital nature [107]. Based on theirFermi surface topology, one could generally divide theminto two categories: 1. systems with both electron andhole Fermi surfaces, and 2. systems with only electronFermi surfaces. Most of the iron pnictides and Fe(Te,Se)bulk materials belong to the first category,[108–112] whileAxFe2−ySe2, single layer FeSe on STO, and heavily elec-tron doped iron pnictides belong to the second category[113–116]. Since most of the iron based superconduc-tors are in the first category, we will discuss its elec-tronic properties in the following first three subsections,while those of the second category will be discussed in thefourth subsection. In the last subsection, we will discussthe role of correlations and some overall understandingsof the electronic structure.

Basic electronic structure

The low energy electronic structure of iron-based su-perconductors are dominated by the Fe 3d states [117].The unit cell contains two Fe ions, because there are pnic-

10

togen and chalcogen ions above and below the iron plane.As a result, there would be totally ten 3d states and thusten bands. However, it was found both by polarization-dependent ARPES experiments and density functionaltheory calculations that the Fermi surface is usually com-posed of three hole-like Fermi surfaces near the zone cen-ter and two electron Fermi surfaces around the zone cor-ner. The dxy, dxz and dyz orbitals are the main contrib-utor to the states near the Fermi energy EF [118, 119].Fig. 9(a) illustrates a typical band structure along the Γ-M direction, and Fig. 9(b) shows the measured Fermi sur-face of BaFe2(As0.7P0.3)2 in its three-dimensional Bril-louin zone [120]. The Fermi surface topology and bandstructure are rather similar for the 11, 111, 122, 1111series of iron-based superconductors [108–112].

Strictly speaking, the iron-based superconductors arethree dimensional materials, however, the electron hop-ping along the c direction is not strong, so that the warp-ing of the Fermi surface along the kz direction is not soobvious for most of the bands. However, the α bandshows strong kz dependence, and its Fermi surface ex-hibits large warping in Fig. 9(b).

The carrier density of iron-based superconductors canbe tuned by doping in the charge reservior layer, or atthe Fe site. Electron and hole doping can be varied overa large range, which in turn varies the chemical potentialand the Fermi surface. Fig. 9(c) shows the hole-dopingevolution of the Fermi surface sheets in Ba1−xKxFe2As2,and the electron-doping evolution of the Fermi surfacesheets in NaFe1−xCoxAs. With sufficient doping, Lifshitztransitions of the Fermi surface topology eventually occurin both cases [116, 121].

In the case of isovalent doping, such as Ru for Fe, P forAs, or Te for Se, the Fermi surface volume usually doesnot change, or change slightly for some unknown reason,but the individual Fermi surface sheets may change no-ticebly by the induced chemical pressure [120, 122]. Theband renormalization factor also generally decreases withdoping, which indicates the weakened correlation.

Compared with the cuprate superconductors, whichis a doped Mott insulator, the iron-based superconduc-tors are less sensitive to impurities. However, the largeamount of dopants will cause serious scattering of thequasiparticles that needs to be taken into account in un-derstanding the transport and SC properties. The dxy-based γ band near the zone center are somehow moresensitive to impurities [116]. The impurity scatteringalso strongly depends on the locations of the dopants,which in the increasing order is off-plane, at the pnicto-gen/chalcogen site, and at the iron site [116, 123].

The nematic phases

The nematic phases here refer to the collinear anti-ferromagnetic (CAF) state, and the orthorhombic phase

Γ M

α β

γ

ηδ

Bin

din

g e

ne

rgy

Momentum

EF

(a)

β

γ

α

ηδ

Γ

Ζ (0, 0, π)Α

hole

electron

kx

ky

kz

Μ (π, 0, 0)

NC4.5 NC14.6NC10 NC32

BK23 BK65BK40 BK86

(c) hole doping

electron doping(d)

SS SSΓ Μ Γ Μ Γ Μ Γ Μ

Γ Μ Γ Μ Γ Μ Γ Μ

Lifshitz transition at M

Lifshitz transition at Γ

(b)

FIG. 9. (a) Cartoon of the band structure in iron-pnictides.(b) The typical three-dimensional Fermi surface of iron-pnictides BaFe2(As0.7P0.3)2 [124]. (c) The doping dependenceof Fermi surface topology taken in Ba1−xKxFe2As2. The up-per panels are the photoemission intensity distribution at EF .The low panels are the obtained Fermi surface. SS is the ab-breviation of surface state. The red and blue lines illustratethe hole pockets and electron pockets, respectively. (d) is thesame as panel (c), but taken in NaFe1−xCoxAs.

below the structural transition temperature Ts, as illus-trated in Fig. 10(a) [125]. There are signs of a ferro-magnetic orbital ordered phase above Ts, which exhibitsnematicity as well.[126, 127] Such a nematicity can beviewed in the resistivity of detwined sample shown inFig. 10(b). STM has found nematic order with large pe-riods, which has not been observed by bulk measurements[128].

In the beginning, the nesting between the electron andhole Fermi surface sheets was considered to be the drivingforce of the CAF state, as it coincide with the (π, 0) or-dering wavevector [67]. As a result, sometimes the CAFstate was called spin density wave. However, it was soonfound that a good nesting often does not correspond to aCAF state [116]. On the other hand, when the hybridiza-tion gap occurs, it is well below EF due to crossing withthe folded bands. Moreover, the entire bands shifts, in-stead of just in the vicinity of the crossing [108, 110].

The evolution of the nematic electronic structure isillustrated with the example of NaFeAs, where the Tsis above the Neel temperature [129]. The sample wasdetwinned with moderate pressure, so that the elec-tronic structure along different directions are disentan-gled, starting from a slightly higher temperature T ′s than

11

-80

-60

-40

-20

100806040200

Pe

ak p

ositio

n (

me

V)

T (K)

dxz

dyz

TN

TS

TS’

βx

βy

ΔH0

(h)

-0.1 0.0

60 K54 K49 K44 K40 K36 K30 K20 K

-0.1 0.0

60 K54 K49 K44 K40 K36 K30 K20 K

Inte

nsity (

arb

. u

nits)

(d) (f)

(e)

0.88 π/a

dxz

dyz

βx

βy

(g)

E-EF (eV)

Inte

nsity (

arb

. u

nits)

k1 Γ Mx

Orthorhombic PM

EF

αy βx

γxγyδy

kx ky ky

k2 MyΓ

ky kx kx

Orthorhombic PM

αx

βy

ηxEF

0.88 π/a

k1

k2

y,

x,AFM

FM

kx

ky

Mx

My

Γ

(b)

ρ (

mΩ

cm

)

T (K)

ρboρao

TN= 43 K

0.20

0.00100806040200

TS’= 75 K

ρ//

0.20

0.00T

S= 54 K

TN= 43 K

Unstressed NaFeAs

100806040200

Uniaxially stressed NaFeAs

(i)

dyz

dxz

NaFeAs

ρ (

mΩ

cm

)

(a)

Fe2

Fe1

Tetragonal PM Orthorhombic CAF

at

bo

aoa

Orthorhombic PM

T > TS

TS > T > T

NT < T

N

bo

ao

NaFeAs

NaFeAs(c)

FIG. 10. (a) Cartoon of the lattice and spin structure in tetragonal paramagnetic (PM), orthorhombic PM, and orthorhombicCAF state for iron-pnictides. The large black arrows show the direction of the uniaxial pressure applied in the mechanicaldetwinning process. (b) The temperature dependent resistivity of unstressed and uniaxially stressed NaFeAs, respectively. (c)The definition of the projected two-dimensional Brillouin zone for NaFeAs. The x and y axes are defined along the iron-irondirections. (d) The band structure in the orthorhombic PM state along Γ-Mx and some other high symmetry directions, whereonly dyz- and dxy-dominated bands are highlighted. (e) is the same as panel (d), but mainly along the Γ-My direction, with thedxz-dominated bands highlighted. (f) and (g) The temperature dependence of the EDCs at k1 and k2, as indicated by the grayline in panels (d) and (e), respectively. (h) The peak positions of the βx and βy bands as functions of temperature. The maximalobservable separation between βx and βy at the same momentum value (i.e. |kx| = |ky|) near Mx and My respectively is definedas ∆H . ∆H is a function of temperature, and its low temperature saturated value is defined as ∆H0. (i) Energy position of thedxz and dyz bands as a function of temperature, measured on both detwinned and unstressed Ba(Fe0.975Co0.025)2As2, comparedwith resistivity measurements.[125] Data are taken from Ref. 129 and Ref. 130.

Ts. As shown in Fig. 10(c), the Γ-Mx and Γ-My arenot equivalent in the nematic phases. The electronicstructure behaves drastically different in these two di-rections (Fig. 10(d,e) in the nematic phases). For theβ band whose dispersions are the same along these twodirections in the tetragonal paramagnetic (PM) phase,its position starts to move in different directions belowT ′s, which is clearly demonstrated by Fig. 10(f-h). Theband position difference (∆H0) saturates at low temper-atures eventually. Similar behavior has been observedin detwinned BaFe2−xCoxAs2 (Fig. 10(i)) as well, show-ing that it generally occurs in different compounds [130].Such a smooth temperature evolution across both thestructural and magnetic transitions indicates that theyare of the same origin, and the nematic phases are char-acterized by the the same electronic structure nematicity[110]. Different phases could be viewed as different stagesof the same evolution. At high temperatures, althoughthe structure is tetragonal, the electronic nematicity al-ready occurs above Ts, the hopping parameters along aand b start to differ. As a result, the occupations ofdxz and dyz orbitals become inequivalent at all Fe sites,which can be viewed as an ferromagnetic orbital order[127], although such a difference could be rather small,just a few percent in the NaFeAs case down to the low-

est temperature [129]. Short ranged or fluctuating CAForder might have occurred, in associated with the ne-maticity. It was suggested that the spin order is moretwo dimensional and more susceptible to fluctuations, sothat the Neel temperature is lower than Ts in some cases[131]. The electronic (spin, charge, orbital) and struc-tural degrees of freedom all participate into this process,so that it is likely difficult and unnecessary to identifywhich is the dominating driving force. Nevertheless, thetotal electronic energy is reduced significantly, which iswell beyond the energy due to the structural change.

The anisotropy of the resistivity in the nematic phase isconsistent with the anisotropic electronic structure, how-ever recent STM measurements showed that the impurityscattering can be rather anisotropic [128]. This explainsthe variations of the resistivity anisotropy in differentcompounds. Further investigations are needed to clarifythis issue.

FeTe is a special parent compound of iron-based su-perconductors, which exhibits a bicollinear antiferromag-netic order [132, 133]. Its polaronic electronic structureis rather different from those of iron pnictides, which isconsistent with its large local moment though [111, 134].The magnetic order in FeTe can be explained by the ex-change interactions amongst local moments as well.

12

-40 -20 0 20 40

29 eV

22 eV

25 eV

27 eV

31 eV32 eV33 eV

34 eV

35 eV

36 eV

37 eV

39 eVα

E-EF (meV)

ky

hυ =Ζ

Γ

kz= π

kz= 0

Inte

nsity (

arb

. u

nits)

4

0

8Gap (meV)

Γ

Ζ Α

Μ

BaFe2(As

0.7P0.3)2

α γ β η δ

(c)

(d)(b)Ba

0.6K

0.4Fe

2As

2

Α

Μ

Ζ

Γ

12

8

4

0

Gap (meV)αγ β η

(a)Ba

0.6K0.4Fe

2As

2

(e)

p

Ζ

s

Ζ

Γ/Ζ Μ/Α

γ

η

δ

Γ/Ζ Μ/Α

δ/η γ

7

6

5

4

Gap (meV)

BaFe2(As

0.7P0.3)2

NaFe0.9825

Co0.0175

As

NaFe0.955Co

0.045As

(f)

θ

2

4

6

2 4 6

|Δ| (meV)

0 θ

2

4

6

2 4 6

α

βγ

δ

0

Γ Μ

|Δ| (meV)

LiFeAs

FIG. 11. (a) The illustration of the in-plane gap distribution on the Fermi surface in Ba0.6K0.4Fe2As2. The inset shows thetemperature dependence of the SC gap. (b) Illustration of the gap distribution on 3D Fermi surface in Ba0.6K0.4Fe2As2. (c) kzdependence of the symmetrized spectra measured on the α hole Fermi surface in BaFe2(As0.7P0.3)2. The dashed line is a guideto the eyes for the variation of the SC gap at different kz values. The inset shows the polarization dependent Fermi surfacemaps around Z, indicating the α pocket around Z is mainly composed of the d2z orbital. (d) Illustration of the gap distributionon the 3D Fermi surface of BaFe2(As0.7P0.3)2. (e) and (f) The in-plane SC gap distribution on LiFeAs and NaFe1−xCoxAs,respectively. Data are taken from Refs. 124, 135, and 213 and Ref. 159.

Superconducting region

Insulating region

KxFe

2-ySe

2

(d)

10

5

∆ (meV)

κ

θ

δ/η

5

10

∆ (meV)

(c)(a)

(b)

θ

Γ

M

A

δ/η

Γ

M

Zκ

FIG. 12. (a) Cartoon for mesoscopic phase separation in SCKxFe2−ySe2. (b) The Fermi surface of the SC phase. (c) Gapdistribution on the δ/η electron pocket around M in polar co-ordinates, where the radius represents the gap, and the polarangle θ represents the position on the δ/η pocket with respectto M, with θ = 0 being the M-Γ direction. (d) is the same as(c), but for the κ pocket. Data are taken from Refs. 114 and170 and Ref. 173.

The SC phase

There are two critical issues in the electronic structureof the SC state: 1. what is the pairing symmetry; and 2.what determines the Tc.

Pairing symmetry is manifested in the SC gap distri-bution. For conventional phonon mediated s-wave su-perconductors, the gap is nodeless, i.e. the Fermi sur-face is fully gapped. While for cuprates, there are nodes(zero gap) along the diagonal directions, reflecting itsd-wave symmetry. However, for iron-based superconduc-tors, there are both nodal and nodeless members [135–144].

Nodeless SC gap

A large fraction of the iron pnictides are nodeless basedon thermal conductivity, penetration depth, STS, andother measurments [145–148]. For such a multi-band sys-tem, the gap amplitudes vary on different Fermi surfacesheets [149]. On individual Fermi surface sheets, the in-plane gap distribution is often isotropic (within the ex-perimental uncertainty), eg. for Ba1−xKxFe2As2 shownin Fig. 11(a). The anisotropy along the kz direction usu-ally is negligible for most Fermi pockets, but some no-ticeable dependence was found for the α Fermi surface

13

ΔH

0 (m

eV

)

50

02001000

TA (K)

150

100

(c)

NaFeAs

NaFe0.9825Co0.0175As

SrFe2As2

Sr0.9K0.1Fe2As2

CaFe2As2

BaFe2As2

Sr0.82K0.18Fe2As2

50 150

FeSe film

200

180

160

140

120

100

80

60

40

20

0

3.93.83.73.63.5

1ML FeSe

bulk FeSe

FeSe film

s

Tem

pera

ture

(K

)

Lattice constant a (Å)

FeSe crystal

Increasing hydrostatic pressure

TA

TC

KxFe

2-ySe

2

FeTe0.5

Se0.5

Lix(NH

2)y(NH

3)1-y

Fe2 Se

2

Superconducting

SDW

FeSe/STO film

Increasing thickness

heavy

electron

doping

(b)

Ord

ere

d m

om

en

t (μB )

-0.2

-0.1

0.0

-0.2

-0.1

0.0

-0.2

-0.1

0.0

-0.2

-0.1

0.0

-0.2

-0.1

0.0

0.0 0.4-0.4

x=0.318

x=0.045

x=0.100

x=0.146

K0.77

Fe1.65

Se2

E-E

F (

eV

)

k// (A-1)

(a1)

kF

kF

kF

kF

kF

1.0

0.5

0

ΔH0

measured by ARPES

Ordered moment

measured by NS

NaFe1-xCoxAs

(a2)

FIG. 13. (a1) The doping dependence of an electron-like bandη around the zone corner for NaFe1−xCoxAs with x=0.045,0.065, 0.146, and 0.318, respectively. (a2) The electron bandsaround the zone corner of K0.77Fe1.65Se2. Note that the pho-ton energies used for different samples are not the same butall correspond to the same kz in the 3D Brillouin zone. (b)Phase diagram of FeSe. The Tc and TA for FeSe are plottedagainst the lattice constants. The right side is based on thinfilm ARPES data, and the left side is based on the transportdata of FeSe single crystal under hydrostatic pressure takenfrom Ref. 214. The dashed line represents the extrapolatedTA’s, which is the temperature when the band starts to re-construct, or become nematic (i.e. TA = T ′s). Values of Tc’sfor other iron selenides are also plotted in the elliptical re-gion. (c) Band separation measured by ARPES and orderedmoment measured by neutron scattering as a function of TA.The dashed line is a guide for the eyes. Data in panel c andd are taken from Ref. 115.

with a sizable warping, as shown in Fig. 11(b). For somecompounds, such as LiFeAs and Fe(Te,Se), in-plane gapdistribution could be anisotropic as plotted in Fig. 11(e), which was attributed to the Fermi surface shape or dif-ferent pairing interactions mediated by various exchangeinteraction terms.

Theoretically, the s±-wave pairing symmetry was pro-posed for the iron-based superconductors [150, 151].However, its proofment requires phase-sensitive tech-niques to detect the phase difference among variousFermi surface sheets. The magnetic field dependenceof the quasiparticle interference pattern of Fe(Te,Se) ob-served by STM was shown to support the s±-wave phase-changing scenario [152].

Nodal SC gap

The nodal SC gap was found in some iron pnictideswith pnictogen height less than 1.33 A, KFe2As2 andFeSe film grown on graphene [141, 143, 144]. As shownin Fig. 11(c-d), the nodal gap of BaFe2(As1−xPx)2 is lo-cated in a ring around Z on the α hole pocket with signif-icant warping and contribution from the dz2 orbital.[124]This indicates its “accidental” appearance, and rules outthe symmetry related origin of the nodes [150, 151]. The-oretically, it has been shown that dz2 does not con-tribute much to pairing [153]. This hole Fermi pocketis from the same α band whose gap shows significantkz dependence in the optimally doped Ba1−xKxFe2As2(Fig. 11(b)), thus similar origin is expected for both.

For KFe2As2 and heavily doped Ba1−xKxFe2As2,laser-ARPES work indicate the gap nodes appear at cer-tain points around Z on a Fermi pocket with strong dz2characters [154], while some other ARPES studies showthat they appear on some small hole pockets near M asvertical nodal lines [155]. Whether these are due to sam-ple dependence or due to the high kz resolution of laser-ARPES needs further clarification. However, the impor-tant message is that the nodes in these compounds areaccidental, and not due to d-wave or other phase chang-ing pairing symmetry. This unites the nodal and nodelessgap behavior in one single scheme.

Gap in CAF/superconductivity coexisting regime

As demonstrated by µSR, neutron scattering andARPES studies, there is a unique SC regime in the phasediagram of iron-based superconductors, where CAF orderand superconductivity coexists [156–160]. Particularly,the recent STM measurements of NaFe1−xCoxAs showsthe microscopic coexistence and competition of these twoorders [161]. The presence of such a unique regime putsstrong constraints on the possible paring symmetry. Forexample, such a coexistence would not be possible, hadthe pairing symmetry been s++-wave type, where thephases of the SC order parameter are the same on var-ious Fermi surface sheets. On the other hand, somecalculations based on the s±-wave pairing suggest thatCAF order would induce strong gap anisotropy; and in-creasing strength of the CAF order, even nodes could beinduced.[162, 163] Consistently, a strong gap anisotropyhas been observed on the electron Fermi surfaces forNaFe1−xCoxAs in the coexisting regime, but not in thepure SC regime (Fig. 11(f)), although their dopings differjust slightly.

This might explain the nodal gap observed in the FeSefilm grown on a graphene substrate by STS, since obvi-ous signs of CAF order or strong fluctuations has beenobserved by the recent ARPES measurements of multi-layer FeSe films grown on STO substrate [115, 144]. As

14

a comparison, the STS measurements show that the gapof Fe(Te,Se) is nodeless, where CAF order is not present[152].

Electronic features correlated or uncorrelated with thesuperconductivity

Tc-determining factors are crucial for understandingthe mechanism of superconductivity in unconventionalsuperconductors. Many empirical observations have beenmade as to what affects the Tc for iron-based supercon-ductors. First of all, it was found that near the optimaldoping of some iron pnictides, certain electron and holeFermi pockets are better nested, namely, they can overlapon each other when shifted [136]. While doped away fromthe optimal doping, the nesting worsens, since electronand hole pockets change differently. However, variouscounter examples have been found later.

In some iron pnictides, such as BaFe2−xCoxAs2 andNaFe1−xCoxAs, it was found that the superconduc-tivity diminishes when the system is doped with suf-ficient electrons so that a Lifshitz transition occurs(specifically, the dxz/dyz based hole pockets disappear)[116, 164]. Such a correlation with the superconduc-tivity suggest the importance of this hole Fermi sur-face. However, later, a counter example is found inCa10(Pt4As8)(Fe2−xPtxAs2)5 (Tc ∼20 K), where onlydxy based hole pocket exists [165]. A likely cause is thatthe dxy-based bands are strongly scattered by Co dopantsin BaFe2−xCoxAs2 and NaFe1−xCoxAs, while it is notstrongly scattered in Ca10(Pt4As8)(Fe2−xPtxAs2)5. Thishighlights the effects of impurity on the superconductiv-ity. Furthermore, Cr, Mn, Cu and Zn dopants at theFe site kill superconductivity much more effectively thanCo and Ni. Their effects on the electronic structure havebeen extensively studied [166, 167].

Electron correlation, or more specifically, spin fluctua-tions is found to correlate with the superconductivity. Itmanifests as the distance from the CAF phase, the bandrenormalization factor, or the dynamical spin susceptibil-ity measured by INS. These general observations suggestthat the superconductivity in iron-based superconductorsare mediated by magnetic interactions. In a local pairingscenario, the gap functions of various iron-based super-conductors were fitted rather well by including exchangeinteractions between nearest neighbours, the next nearestneighbours, and the next next nearest neighbours [168].

So far, a more quantitative correlation between cer-tain electronic properties and superconductivity remainslacking, besides that the SC gap generally scales withTc. This illustrates the complexity of the problem, andrequires further systematic work

AxFe2−ySe2 and FeSe thin films

AxFe2−ySe2 and single layer FeSe thin film grown onthe STO substrate are the two known iron-based super-conductors with only electron Fermi surface [114, 115,169]. Heavily electron-doped iron pnictides have onlyelectron pocket, however, they are non-SC, as the spinfluctuations diminishes [121]. These two chalcogenideswith unique electronic structure and rather high Tc posechallenges on the physical pictures established previouslyfor systems with both electron and hole Fermi surfacesheets.

AxFe2−ySe2

The SC AxFe2−ySe2 sample is phase separated, con-taining iron-vacancy ordered insulating domains and SCdomains in nanometer scale, as illustrated in Fig. 12(a).The electronic structure of the insulating phase behaveslike a Mott insulator. A semiconducting domain wasfound in some materials, whose band structure is similarto that of the SC domain, except all the bands are filled.The phase separation was observed both by ARPES andSTM, among other measurements [170–172].

For the SC phase, the Fermi surface of KxFe2−ySe2 isshown in Fig. 12(b). The two electron Fermi surfacesaround the zone corner cannot be resolved, and there isa small κ electron pocket around Z.[114] The gap distri-butions on these Fermi surfaces are isotropic as shownFig. 12(c)(d) [173]. This and the neutron resonance peak[174], pose severe challenges on theory regarding whatkind of pairing symmetry presents in this system.

FeSe/STO thin films

The likely high Tc of 65 K in the single layer FeSe/STOfilm has raised a lot of interest [14, 115, 169]. The largestand isotropic SC gap has been obsered by ARPES andSTS. The FeSe is found to be doped by electron trans-ferred from the oxygen vacancy states in the STO sub-strate [115]. The superconductivity is found only in thefirst layer on the substrate. For multi-layer FeSe film,which is undoped, there are both electron and hole Fermisurfaces, and the electronic structure reconstruction cor-responding to the CAF order is observed [115].

By further expanding the FeSe lattice withFeSe/STO/KTO heterostructure, the two electronFermi pockets become more elliptical and resolvable[175]. The lack of hybridization between them, andthe strong gap anisotropy provide more constraints ontheory, suggesting sign change in Fermi sections andinterband pair-pair interactions [176]. The gap closesaround 70 K in FeSe/STO/KTO, even now 75 K for

15

FeSe/BTO/KTO film [177], indicating a new route toenhance the superconductivity.

The critical role of correlations

Electron correlation is manifested in the band renor-malization factor of the iron-based superconductors.Fig. 13(a1) illustrates the evolution of dispersion inNaFe1−xCoxAs, the band becomes much lighter with in-creased doping. In the heavily electron-doped case, thecorrelation (or spin fluctuation here) is very weak, asthey are far away from the CAF phase. As a result, theyare non SC. However, its Fermi surface is very similarto that of KxFe2−ySe2, but the latter has a much largerband mass or narrow bandwidth (Fig. 13(a2)), and a Tcaround 30 K. The strong correlation in KxFe2−ySe2 islikely related to its large lattice constant, since for themultilayer FeSe films, it was found that the CAF or-dering strength increases with increased lattice constant(Fig. 13(b)). These FeSe films are under high tensilestrain, whose lattice constants are much larger than thatof bulk FeSe [115].

The electronic structure is itinerant in most of the ironbased superconductors. However, there are an effectivelocal moment [134], and the coupling between the itiner-ant electrons and local moments (which are the two sidesof the same coin) gives the Hund’s rule coupling, themain correlation source in these compounds [178, 179].Such a Hund’s metal behavior is also responsible for theCAF order in these materials. In fact, the energy scale ofthe electronic structure reconstruction is found to scalewith the Ts/TN and the local moment measured by theneutron scattering Fig. 13(c) [58, 115, 180–189].

Local moments are important for superconductivity aswell. Take systems like the collapsed-tetragonal (cT)phase as an example, where core-electron spectroscopyindicates the absence of local moments, the superconduc-tivity disappears, and bands become less correlated. Theelectronic structure of the cT phase is similar to that ofBaFe2P2, where the small lattice constants enhance thehopping and thus the itineracy. Relatedly, for the singlelayer FeSe/STO film or AxFe2−ySe2, their superconduc-tivity should be related to the enhanced correlations bythe expanded lattice.

Assuming the superconductivity of all the iron-basedsuperconductors is due to one unified mechanism, the re-sults obtained on the above two categories of compoundsactually would help to sort out the SC mechanism. Thegap is generally isotropic and nodeless (nodes being ac-cidental) in these systems, although there could be signchanges in different Fermi pockets or sections. The dra-matic difference in the Fermi surface topologies indicatesthat the pairing is local in the real space, mediated byshort range antiferromagnetic interactions.

Finally, we note that although a general experimental

phenomenology has been established, there are still manyremaining open issues to be addressed. For example, inthe recent FeSe/STO studies, it was suggested that theinterface has a non-trivial role on the superconductivity,and particularly the interfacial phonon might play an im-portant role [177, 190].

16

THEORY

Theory of high-Tc superconductivity remains one ofthe most fundamental and challenging problems. TheBCS theory fails to explain why the SC transition tem-peratures for both cuprate and iron-based superconduc-tors can be much higher than the possible upper limit forelectron-phonon mediated superconductors (40 K) [191].The highest Tc ∼ 55 K of iron-base superconductors [6] isstill much lower than that for the cuprate superconduc-tors (164 K under high pressure). However, the study forthe iron-based superconductivity is of particular interestbecause (1) Fe2+ ions have magnetic moments which aregenerally believed to be detrimental to superconductiv-ity, the discovery of high-Tc superconductivity in ironpnictides has overturned this viewpoint and opens a newdirection for exploring new superconductors; (2) thereare strong AF fluctuations in iron-based superconduc-tors and the investigation to these materials may helpus to understand more deeply the pairing mechanism ofhigh-Tc superconductivity in general.

Iron-based superconductors, including iron pnictidesand iron chalcogenites, are quasi-two-dimensional mate-rials. They have very complicated electronic structuresand competing interactions. To understand the mecha-nism of iron-based superconductivity, the first task is toestablish the minimal model to describe the low energyelectronic excitations in these materials. A key issue un-der debate is whether the system is in the strong or weakcoupling limit, since the interaction that drives electronsto pair can be very different in these two limits.

Band structure

From first principles density functional theory (DFT)calculations, we know that the low energy excitations ofelectrons in iron-based superconductors are mainly con-tributed by Fe 3d electrons. At high temperatures, ironpnictides/chalcogenides are paramagnetic metals. Atlow temperatures, most of parent compounds, includingLaFeAsO, BaFe2As2 and other 1111 and 122 pnictides,FeTe, are in the AF metallic phase. They become SCupon electron or hole doping. For LaFePO, LiFeAs orother 111 pnictides, the parent compounds without dop-ing are SC at low temperatures.

As an example, Fig. 14 shows the Fermi surface andthe band structure for BaFe2As2 in the high tempera-ture paramagnetic phase [192]. Similar band structuresare found for other iron pnictides [193, 194] and chalco-genides [133]. In general, there are five bands across theFermi surface. Among them are two electron-like Fermisurfaces centered around M = (π, 0) and its equivalentpoints and two hole-like Fermi surfaces centered aroundthe zone center Γ = (0, 0). For 1111 or hole doped 122materials, in addition to the above four surfaces, there

is one more hole-like Fermi surface appearing around Z.This band is more three-dimensional like than the otherfour bands and shows a large energy-momentum disper-sion along the c-axis. The band structure of the single-layer FeSe grown on SrTiO3 substrate is relatively simple[195]. There are only two bands, located around (π, 0)and (0, π), across the Fermi level [196]. The qualitativefeature of the band structures obtained by the DFT cal-culation agrees with the ARPES measurements. But theband width and the effective mass of electrons aroundthe Fermi surface are found to be strongly renormalizedby correlation effects which are ignored in the DFT cal-culation.

Minimal model for describing iron-basedsuperconductivity

Our discussions on minimal model below will be basedon strong coupling point of view, where we consider theelectron interaction is strong. The weak coupling view-point starts with itinerant electrons and treats electroninteraction as a perturbation. The weak coupling theo-ries may explain a number of experiments in iron-basedsuperconductivity [26, 27]. However, they have difficultto explain local magnetic moments and superconductiv-ity in systems without Fermi surface nesting. Amongthe five 3d orbitals of Fe ions, dxz, dyz and dxy con-tribute most to the low energy excitations. These or-bitals couple strongly with each other and with the othertwo Fe 3d orbitals, dx2−y2 and dz2 , by the Hund’s ruleexchange interaction. In the atomic limit, an Fe2+ ionpossesses a large magnetic moment, ∼ 4µB , with a totalspin S = 2. When Fe atoms form a crystal by hybridiz-ing with As and other atoms, these 3d electrons maybecome itinerant. If all 3d orbitals of Fe become highlyitinerant, one would expect that the magnetic moment of

FIG. 14. (a) Electronic band structure and (b) band structurein the paramagnetic phase for BaFe2As2 in the folded Bril-louin zone. (c) and (d) are the sectional views of the Fermisurface through symmetrical k-points Z and Γ perpendicularto the z-axis, respectively. (From Ref. [192]).

17

Fe will be completely quenched. However, neutron andother experimental measurements indicate that the mag-netic moments of Fe remain finite at least for most ofundoped or slightly doped iron pnictides/chalcogenides[58, 132, 197]. For example, the ordering moment of Fein the antiferromagnetic ordered state is about 0.37µBfor LaFeAsO [58], 2µB for FeTe [132] and 3.31µB forK2Fe4Se5 [197]. It should be pointed out that the Fermisurface nesting effect cannot give such a large orderingmoment and the magnetic moment of Fe must have thecontribution from electrons whose energy is well belowthe Fermi level [192]. The total moment of an Fe ion isa sum of the ordering moment and the fluctuating mo-ment. The fluctuating moment results from thermal andquantum fluctuations of Fe moment and is zero on aver-age. A small ordering moment does not mean the totalmoment of an Fe spin is also small. The total momentsin most of 1111 and 122 pnictides can in fact be muchlarger than the ordering moments, which suggests strongquantum fluctuation in the parent compounds.

The existence of Fe moments in these materials meansthat not all Fe 3d electrons are equally conducting, someof them are more localized than the others. From the firstprinciples density functional calculation, it was foundthat the crystal splitting of the 3d orbitals is small, butthe hybridization between Fe and As/Se atoms and theon-site Coulomb interaction vary differently for different3d orbitals. This may lead to an Hund’s rule couplingassisted orbital selective Mott transition [198] and allo-cate a finite magnetic moment for each Fe by localizingsome 3d orbitals. Thus Fe 3d electrons possess both localand itinerant nature. The low energy charge dynamics isgoverned by itinerant 3d electrons and behaves more likein a conventional metal with weak correlation, whereasthe spin dynamics is essentially governed by localized mo-ments and behaves more like in a strong coupling system.Moreover, these itinerant electrons and local moment arenot independent, they are actually coupled together bythe Hund’s rule coupling. This is similar as in a colossalmagnetoresistance (CMR) manganate where the doubleexchange interaction induced by the Hund’s coupling be-tween localized and itinerant electrons is important. Ofcourse, the Coulomb screening of conduction electrons tothe local moments is stronger in Fe-based materials. Thismay explain why the magnetoresistance is fairly large inthe antiferromagnetic ordered phase in FeTe or other Fepnicides materials.

Iron-based materials exhibit various antiferromagneticorders. These orders are driven predominantly by themagnetic interactions between Fe spins, among them themost important one is the superexchange interaction be-tween Fe spins mediated by As or Se 4p electrons [194].The superexchange interaction depends on the hybridiza-tion between 3d and 4p orbitals, in particular on the bondlength and the angle of Fe-As-Fe. Besides this, there isalso a direct ferromagnetic exchange interaction between

two Fe ions, which is determined by the wavefunctionoverlap between two 3d orbitals on the two neighboringFe sites. These exchange interactions are short rangedwhich extends mainly to the nearest and next nearestneighbors for Fe pnictides or Fe selenides, and to the thirdnext-nearest neighbors for Fe tellurides [193, 194, 199].

The above discussion suggests that the minimal modelfor describing iron-based superconductors is approxi-mately given by [192, 198]

H =∑ij,αβ

tαβij c†α,icβ,j + J1

∑〈ij〉

Si · Sj

+J2∑〈〈ij〉〉

Si · Sj , (1)

where α and β are the orbital quantum number of itin-erant electrons, and Si =

∑α c†α,iσcα,i/2. The first term

is the tight binding Hamiltonian of itinerant electrons.The second and third terms are the exchange interac-tions between Fe spins on the nearest and next nearestneighboring sites, respectively. If one ignores the chargefluctuation and considers only the spin dynamics, thisHamiltonian reduces to the J1 − J2 model [193, 194].In this case, the ground state is collinear AF orderedif J2 > J1/2. This is indeed the AF order that is ob-served by neutron scattering measurements [58] in mostof the parent compounds of iron-based superconductors.In passing we note that the minimal model approximatesthe spin-spin couplings independent of the five d-orbital,and has not included Hund’s rule interaction.

In iron-based superconductors, the difference betweencenter momenta for the electron and hole bands, i.e. Mand Γ, coincides with the characteristic wave vector ofthe J2 term. Thus the J2 term couples strongly with theelectron and hole Fermi surfaces. This term is believedto play an important role in driving both AF and SC or-ders. If the hole and Fermi surfaces are perfectly nested,then the J2 coupling will be strongly amplified in thephase space integration, leading to certain Fermi surfacenesting effect, such as the spin density wave instability.Doping can change the phase space that is connected bythe nesting vector, which can strengthen SC order andweaken AF order, or vice verse. In general, the compe-tition between SC and AF correlations is strong in thesematerials. The SC order emerges when the AF order issuppressed.

Gap symmetry and structure

In a SC phase, quantum fluctuations are suppressed bythe SC long range order and the BCS mean field approx-imation is valid. The pairing gap of electrons is an orderparameter characterizing a SC state. Physical propertiesin a SC state can be well described by the BCS theoryonce the gap function is known. This is the reason why

18

the gap function is of particular interest for study. Whilea non-s-wave symmetry may indicate unlikely phononmediated pairing, the pairing symmetry alone is not suf-ficient to determined the pairing interaction.

The gap symmetry is determined by the pairing in-teraction. If the pairing is induced by electron-phononinteraction, it is generally expected that the energy gaphas s-wave symmetry. On the other hand, if the pairingis induced by AF fluctuations, a spin singlet d-wave (forexample in high-Tc cuprates) or spin triplet p-wave (forexample in Sr2RuO4) pairings are possible, dependingstrongly on the band structure, especially on the struc-ture of Fermi surfaces. This is because the SC pairingis a low energy effect and involves only excitations ofelectrons around the Fermi surface. For the same pair-ing interaction, the gap symmetry may change with thechange of the Fermi surface.

The gap symmetry is classified according to thepoint group of crystal. Theoretical study sug-gested that the pairing gap of iron-based supercon-ductors has conventional s-wave symmetry [151, 200–202], namely in the identity representation of pointgroup. This has been confirmed by spectroscopy andtransport measurements on most of iron-based super-conductors including Ba1−xKxFe2As2, BaFe2−xCoxAs2,KxFe2−xSe2, and FeTe1−xSex. However, for KFe2As2,BaFe2−xRuxAs2, and nearly all phosphorus-based super-conductors, LaFePO, LiFeP, and BaFe2As2−xPx, it wasfound that gap nodes exist. The presence of gap nodesgenerally implies that the pairing symmetry is unconven-tional, although an extended s-wave pairing may haveaccidental nodes on one or more Fermi surfaces.

Fe-base superconductors are multi-band systems.There are several bands across the Fermi level. Evenif we assume that the pairing has s-wave symmetry, therelative phases of gap functions can be different on differ-ent Fermi surface, depending on inter-band pairing am-plitudes to be attractive or repulsive. If the gap functionhas the same phase on all the Fermi surfaces, the pair-ing is said to have s++ symmetry. On the other hand, ifthe gap function has opposite phases on different Fermisurfaces, the pairing is said to have s+− symmetry.

The relative phase of the gap function is determined bythe interaction between Cooper pairs on different bands.For iron-based superconductors, if the pairing is inducedby the AF fluctuations, interaction between Cooper pairson the electron and hole bands will generally be repul-sive. In this case, the SC phases are opposite on thehole and electron Fermi surface, and the gap function hass+− symmetry [151, 200–203]. However, if the pairing isinduced by the orbital fluctuation and the SC instabil-ity happens in the A1g channel, the interaction betweenCooper pairs on the electron and hole bands is attrac-tive, and the gap function will have s++ symmetry [204].Thus, from the relative phases in the gap function, onecan determine whether the SC pairs are glued by AF

fluctuations or by orbital fluctuations.In the literature, there are quite many discussions on

the phase structure of the gap function. However, thisphase structure is not in the angular orientation, and isnot sensitive to most experiments. It is actually very dif-ficult to resolve unambiguously this seemly simple phaseproblem [205]. For a s+− superconductor, it is expectedthat a strong neutron resonance peak exists around themomentum linking hole and electron Fermi surfaces, i.e.at M = (π, 0) and equivalent points. This resonancepeak has in fact been observed in nearly all iron-basedsuperconductors [206, 207], lending strong support to thetheory that predicts the pairing to have s+− symmetry.From the experimental observation of quantum interfer-ence of quasiparticles with magnetic or nonmagnetic im-purities, it was also found that a s+− pairing is morelikely [152]. On the other hand, from Anderson theo-rem, it is well known that non-magnetic impurity scat-tering does not affect much on the transition temperaturefor s++ superconductors, but it may reduce strongly thetransition temperature for s+− superconductors. In par-ticular, the transition temperature of a s+− supercon-ductor should decrease with increasing impurity concen-tration. However, for iron-based superconductors, thecritical transition temperature does not depend much onthe quality of samples. This seems to suggest that thes++ pairing is more favored. More systematic study ofvarious impurity effects provides mixed information [208],which may suggest non-universal behavior on the relativephases in iron-based superconductors, in contrast to theuniversal d-wave pairing in high Tc cuprates.

The SC and AF orders are two competing orders. Gen-erally they repel each other. However, if the pairinghas s+− symmetry, theoretical calculation suggested thatthese two kinds of orders can coexist [209]. Experimen-tally, this kind of coexistence has indeed been observedin BaFe2As2, Ba1−xKxFe2As2 and SmFeAsO1−xFx withCo substituting Fe or with P substituting As [73, 210],and in KxFe2Se2. But in these systems in which the co-existence was observed, the SC gap was also found tohave line nodes. It is unknown whether the coexistenceis caused by the s+− pairing symmetry or by the linenodes, or the other way around.

19

SUMMARY AND PERSPECTIVE

In this article, we have reviewed a number of physi-cal properties of iron-based superconductor. During thepast six years, tremendous progress has been achievedin the synthesis of materials, growth of single crystals,characterization of crystal structures, and measurementsof thermodynamics, transport and various spectroscopicquantities for iron-based superconductors. This has givenus a comprehensive understanding on the chemical andcrystal structures, band structures, spin and orbital or-derings, pairing symmetry and other physical propertiesof iron-based superconductors. In particular, the normalstates of Fe-based superconductors have multiple Fermisurfaces including electron Fermi pockets and hole Fermipockets. This indicates importance of multi-orbitals inthese materials. Fe-based superconductors are proximateto antiferromagnetism, which suggests that AF fluctua-tions are responsible for the observed superconductivity.

Studies on the mechanism of iron-based superconduc-tivity is an important part of research on the mechanismof high-Tc superconductivity. Any progress in this di-rection may have strong impact on the study of theoryof strongly correlated quantum systems. To investigatethe SC mechanism, one needs to find out the microscopicorigin that causes the pairing of electrons and establisha theory that is capable to explain existing experimen-tal data and to predict new experimental effects. Thisremains a challenging task. Similar to the cuprate super-conductivity, iron-based superconductivity is generallybelieved to originate pre-dominantly from the electron-electron repulsive interaction, which induces AF fluctua-tions. Superconductivity induced by AF fluctuation hasrecently been reviewed by Scalapino [69]. In the presenttheories based on AF fluctuation, one approximates thepairing vertex solely in terms of the exchange of AF fluc-tuations. This should be reasonable in some cases suchas heavy fermion superconductivity, where the SC stateis near the AF quantum critical point. In cuprates, thereis also the Mott physics. In iron based SC materials,we have argued that the systems are in strong couplinglimit. Furthermore, the system may well have orbital se-lected Mott physics. Theoretical description of high Tcsuperconductivity in both cuprate and iron based super-conductivity remains a grant challenge.

Iron based superconductors are multi-band materials.All five 3d orbitals of Fe hybridize strongly with As or Se4p orbitals. They also couple strongly with each otherand have contribution to both itinerant conducting elec-trons and localized magnetic moments. This brings muchcomplexity to the understanding and explanation of ex-perimental phenomena. We are lacking a clear physicalpicture with reliable theoretical tools to treat an elec-tronic system with strong coupling between itinerant andlocalized electrons. Theoretical study for iron-based su-

perconductors relies more on phenomenological analysisof experimental observations and on various approxima-tions.

In short, the iron-based SC mechanism is a challengingproblem. To solve this problem, we need to further im-prove the quality of single crystals and the resolution ofmeasurements. Besides the routine measurements andcharacterizations, it is more important to design andcarry out smoking gun experimental measurements tosolve a number of key problems, for example the problemwhether the gap function has the s+− symmetry. Thiswill reduce greatly the blindness in the theoretical studyand leads to a thorough understanding of iron-based su-perconductivity.

Fe-based materials have highest SC Tc next to cuprate.Their discovery has greatly encouraged search for othersuperconductors with higher Tc. While we are still farfrom the stage to predict high Tc materials, there is goodprogress along this development. It is possible in futurethat theory may guide the search or synthesis of the highTc superconductors.

ACKNOWLEDGEMENT

We thank our collaborators in high Tc superconductiv-ity and the colleagues attending Beijing Forum of High-Tc for numerous stimulating discussions over the years.This work is in part supported by National Science Foun-dation of China and Ministry of Science and Technol-ogy. PD is also supported by the US NSF DMR-1308603and OISE-0968226. XHC, DLF, and FCZ would like tothank Collaborative Innovation Center of Advanced Mi-crostructures, Nanjing, China. We wish to acknowledgeYan Zhou and Xingye Lu for their helpful assistance inthe preparation of this manuscript.

[1] Bednorz, JG and Muller, KA. Possible high TC super-conductivity in the BaLaCuO system. Z Phys B 1986;64: 189.

[2] Wu, MK, Ashburn, JR and Torng, CJ et al. Supercon-ductivity at 93 K in a new mixed-phase YBaCuO com-pound system at ambient pressure. Phys Rev Lett 1987;58: 908.

[3] Kamihara, Y, Watanabe, T and Hirano, M et al. Iron-Based Layered Superconductor LaO1−xFxFeAs (x =0.05-0.12) with Tc = 26 K. J Am Chem Soc 2008; 130:3296.

[4] Chen, XH, Wu, T and Wu, G et al. Superconductivityat 43 K in SmFeAsO1−xFx. Nature 2008; 453: 761.

[5] Chen, GF, Li, Z and Wu, Z et al. Superconductivityat 41 K and Its Competition with Spin-Density-WaveInstability in Layered CeO1−xFxFeAs. Phys Rev Lett2008; 100: 247002.

20

[6] Ren, ZA, Lu, W and Yang, J et al. Superconductivityat 55 K in iron-based F-doped layered quaternary com-pound SmO1−xFxFeAs. Chin Phys Lett 2008; 25: 2215.

[7] Ren, ZA, Yang, J and Lu, W et al. Superconductivityin the iron-based F-doped layered quaternary compoundNdO1−xFxFeAs. Europhys Lett 2008; 82: 57002.

[8] Wang, C, Li, L and Chi, S et al. Thorium-doping-induced superconductivity up to 56 K inGd1−xThxFeAsO. Europhys Lett 2008; 83: 67006.

[9] Wen, HH, Mu, G and Fang, L et al. Superconductivityat 25K in hole-doped (La1−xSrhx)OFeAs, Europhys Lett2008; 82: 17009.

[10] Rotter, M, Tegel, M and Johrendt, D. Superconductiv-ity at 38 K in the Iron Arsenide (Ba1−xKx)Fe2As2. PhysRev Lett 2008; 101: 107006.

[11] Hsu, FC, Luo, JY and Yeh, KW et al. Superconductivityin the PbO-type structure α-FeSe. Proc Natl Acad Sci2008; 105: 14262.

[12] Wang, XC, Liu, QQ and Lv, YX et al. The superconduc-tivity at 18 K in LiFeAs system. Solid State Commun2008; 148: 538.

[13] Parker, DR, Pitcher, MJ and Baker, PJ et al. Structure,antiferromagnetism and superconductivity of the lay-ered iron arsenide NaFeAs. Chem Commun 2009; 2009:2189-2191.

[14] Wang, QY, Li, Z and Zhang, WH et al. Interface-Induced High-Temperature Superconductivity in SingleUnit-Cell FeSe Films on SrTiO3. Chinese Phys. Lett.2013; 29: 037402.

[15] Anderson, PW. The resonating valence bond state inLah2CuOh4 and superconductivity. Science 1987; 235:1196.

[16] Anderson, PW, Lee, PA and Randeria, M et al.The physics behind high-temperature superconductingcuprates: the ’plain vanilla’ version of RVB. J Phys :Condens Matter 2004; 16: R755-R769.

[17] Lee, PA, Nagaosa, N and Wen, XG. Doping a Mott in-sulator: Physics of high-temperature superconductivity.Rev Mod Phys 2006; 78:17-85.

[18] Rice, TM, Yang, KY and Zhang FC. A phenomenologi-cal theory of the anomalous pseudogap phase in under-doped cuprates. Rep. Prog. Phys. 2012; 75: 016502.

[19] Haule, K, Shim, JH and Kotliar, G. Correlated elec-tronic structure of LaO1−xFxAs. Phys. Rev. Letts. 2008;100: 226402.

[20] Zhang, FC and Rice, TM. Effective Hamiltonian forsuperconducting copper oxides. Phys Rev B 1988; 37:3759.

[21] Johnston, DC. The puzzle of high temperature super-conductivity in layered iron pnictides and chalcogenides.Adv Phys 2010; 59: 803.

[22] Stewart, GR. Superconductivity in iron compounds. RevMod Phys 2011; 83: 1589.

[23] Dagotto, E. The unexpected properties of alkali metaliron selenide superconductors. Rev Mod Phys 2013; 85:849-867.

[24] Dai, PC, Hu, JP and Dagotto, E. Magnetism and itsmicroscopic origin in iron-based high temperature su-perconductors. Nat Phys 2012; 8: 709.

[25] Paglinone, J and Greene, RL. High temperature super-conductivity in iron-based materials, Nat Phys 2010; 6:645.

[26] Hirschfeld, PJ, Korshunov, MM, and Mazin, II. Gapsymmetry and structure of Fe-based superconductors,

Rep. Prog. Phys. 2011; 74: 124508.[27] Chubukov, AV. Paring mechanism in Fe-based super-

conductors. Annu. Rev. Condens. Matter Phys. 2012;3: 13.

[28] Wang, AF, Luo, XG and Yan, YJ et al. Phase Dia-gram and Calorimetric Properties of NaFe1−xCoxAs.Phys Rev B 2012; 85: 224521.

[29] Izyumov, YA and Kurmaev, EZ. FeAs systems: a newclass of high-temperature superconductors. Physics -Uspekhi 2008; 51: 1261 - 1286.

[30] Tegel, M, Johansson, S and Weiss, V et al. Synthesis,crystal structure and spin-density-wave anomaly of theiron arsenide-fluoride SrFeAsF. Europhys Lett 2008; 84:67007.

[31] Matsuishi, S, Inoue, Y and Nomura, T et al. Supercon-ductivity Induced by Co-Doping in Quaternary Fluo-roarsenide CaFeAsF. J Am Chem Soc 2008; 130: 14428.

[32] Hanna, T, Muraba, Y and Matsuishi, S et al. Hydrogenin layered iron arsenides: Indirect electron doping toinduce superconductivity. Phys Rev B 2011; 84: 024521.

[33] Matsuishi, S, Inoue, Y and Nomura, T et al. Effect of3d transition metal doping on the superconductivity inquaternary fluoroarsenide CaFeAsF. New J Phys 2009;11: 025012.

[34] Takahashi, H, Tomita, T and Soeda, H et al.High-Pressure Studies for Hydrogen SubstitutedCaFeAsF1−xHx and SmFeAsO1−xHx. J Supercond NovMag 2012; 25: 1293.

[35] Wu G, Xie YL and Chen H et al. Superconductivityat 56 K in samarium-doped SrFeAs. J. Phys. Condens.Mat. 2009; 21: 142203.

[36] Lu, XF, Wang, NZ and Zhang, GH et al. Supercon-ductivity in LiFeO2Fe2Se2 with anti-PbO-type spacerlayers. Phys Rev B 2013; 89: 020507(R).

[37] Wu, G, Chen, H and Wu, T et al. Different resistivityresponse to spin density wave and superconductivity at20 K in Ca1−xNaxFe2As2. J Phys Condens Matt 2008;20: 422201.

[38] Ronning, F, Klimczuk, T and Bauer, ED et al. Synthe-sis and properties of CaFe2As2 single crystals. J PhysCondens Matt 2008; 20: 322201.

[39] Sasmal, K, Lv, B and Lorenz, B et al. SuperconductingFe-Based Compounds (A1−xSrx)Fe2As2 with A=K andCs with Transition Temperatures up to 37 K. Phys RevLett 2008; 101: 107007.

[40] Guo, J, Jin, S and Wang, G et al Superconductivityin the iron selenide KxFe2Se2 (0≤x≤1.0), Phys Rev B2010; 82, 180520(R).

[41] Krzton-Maziopa, A, Shermadini, Z and Pomjakushina,E et al. Synthesis and crystal growth of Cs0.8(FeSe0.98)2:a new iron-based superconductor with Tc = 27 K. JPhys Condens Matt 2011; 23: 052203.

[42] Wang, AF, Ying, JJ and Yan, YJ et al. Superconduc-tivity at 32 K in single-crystalline RbxFe2−ySe2. PhysRev B 2011; 83: 060512.

[43] Fang, MH, Wang, HD and Dong, CH et al. Fe-based su-perconductivity with Tc=31 K bordering an antiferro-magnetic insulator in (Tl,K)FexSe2. Europhys Lett 2011;94: 27009.

[44] Lv, B, Deng, LZ and Gooch, M et al. Unusual super-conducting state at 49 K in electron-doped CaFe2As2 atambient pressure. Proc Natl Acad Sci 2011; 108: 15705-15709.

21

[45] Yakita, H, Ogino, H and Okada, T et al. A New Lay-ered Iron Arsenide Superconductor: (Ca,Pr)FeAs2. JAm Chem Soc 2014; 136: 846-849.

[46] Ying; TP, Chen, XL and Wang, G et al. Observation ofsuperconductivity at 30∼46K in AxFe2Se2 (A = Li, Na,Ba, Sr, Ca, Yb, and Eu) Sci Rep 2010; 2: 426.

[47] Burrard-Lucas, M, Free, DG and Sedlmaier, SJ et al.Enhancement of the superconducting transition tem-perature of FeSe by intercalation of a molecular spacerlayer. Nat Mater 2013; 12: 15.

[48] Scheidt, EW, Hathwar, VR and Schmitz, D et al. Su-perconductivity at Tc = 44 K in LixFe2Se2(NH3)y. EurJ Phys B 2012; 85: 279.

[49] Krzton-Maziopa, A, Pomjakushin, EV and Pom-jakushin, VY et al. Synthesis of a new alkali metal-organic solvent intercalated iron selenide superconduc-tor with Tc ∼45 K J Phys Condens Matt. 2012; 24:382202.

[50] Zhu, XY, Han, F and Mu, G et al. Sr3Sc2Fe2As2O5 asa possible parent compound for FeAs-based supercon-ductors. Phys Rev B 2009; 79: 024516.

[51] Xie, YL, Liu, RH and Wu, T et al. Structure andphysical properties of the new layered oxypnictidesSr4Sc2O6M2As2 (M=Fe and Co). Europhys Lett 2009;86: 57007.

[52] Ogino, H, Sato, S and Kishio, K et al. Homologous seriesof iron pnictide oxide superconductors with extremelythick blocking layers. Appl Phys Lett 2010; 97: 072506.

[53] Ogino, H, Machida, K and Yamamoto, A et al. A newhomologous series of iron pnictide oxide superconduc-tors (Fe2As2)(Can+2(Al, Ti)nOy) (n =2, 3, 4). Super-cond Sci Technol 2010; 23: 115005.

[54] Ogino, H, Shimizu, Y and Ushiyama, K et al. Super-conductivity Above 40 K Observed in a New Iron Ar-senide Oxide (Fe2As2)(Ca4(Mg,Ti)3Oy). Appl Phys Ex-press 2010; 3: 063103.

[55] Kakiya, S, Kudo, K and Nishikubo, Y etal. Superconductivity at 38 K in Iron-BasedCompound with Platinum-arsenide LayersCa10(Pt4As8)(Fe2−xPtxAs2)5. J Phys Soc Jpn 2011;80: 093704.

[56] Ni, N, Jared, MA and Chan, BC et al. HighTc electron doped Ca10(Pt3As8)(Fe2As2)5 andCa10(Pt4As8)(Fe2As2)5 superconductors with skut-terudite intermediary layers. Proc Natl Acad Sci 2011;108: E1019.

[57] Sun, YL, Jiang, H and Zhai, HF et al. Ba2Ti2Fe2As4O:A New Superconductor Containing Fe2As2 Layers andTi2O Sheets. J Am Chem Soc 2012; 134: 12893.

[58] De la Cruz, C, Huang, Q, and Lynn JW et al. Magneticorder close to superconductivity in the iron-based lay-ered LaO1−xFxFeAs systems. Nature 2008; 453: 899-902.

[59] Nomura, T, Kim, SW and Kamihara, Y et al. Crystallo-graphic phase transition and high-Tc superconductivityin LaFeAsO:F. Supercond Sci Technol 2008; 21: 125028.

[60] Luo, YK, Tao, Q and Li, YK et al. Evidence of mag-netically driven structural phase transition in RFeAsO(R=La, Sm, Gd, and Tb): A low-temperature x-raydiffraction study. Phys Rev B 2009; 80: 224511.

[61] Margadonna, S, Takabayashi, Y and McDonald, MT etal. Crystal structure and phase transitions across themetal-superconductor boundary in the SmFeAsO1−xFx(0 6 x 6 0.20) family. Phys Rev B 2009; 79: 01450.

[62] Huang, Q, Qiu, Y and Bao, W et al. Neutron-diffractionmeasurements of magnetic order and a structural tran-sition in the parent BaFe2As2 compound of FeAs-basedhigh-temperature superconductors. Phys Rev Lett 2008;101: 257003.

[63] Mizuguchi, Y, Hara, Y and Deguchi, K et al. Anionheight dependence of Tc for the Fe-based superconduc-tor. Supercond Sci Technol 2010; 23: 054013.

[64] Lee, CH, Kihou, K and Iyo, A et al. Relationship be-tween crystal structure and superconductivity in iron-based superconductors. Solid State Commun 2012; 152:644.

[65] Zhao, J, Huang, Q and de la Cruz, C et al. Struc-tural and magnetic phase diagram of CeFeAsO1−xFxand its relation to high-temperature superconductivity.Nat Mater 2008; 12: 953.

[66] Shirage, PM, Miyazawa K and Ishikado, M et al. High-pressure synthesis and physical properties of new iron(nickel)-based Superconductors. Physica C 2013; 469:355-369.

[67] Dong, J, Zhang, HJ and Xu, G et al. Competing ordersand spin-density-wave instability in La(O1−xFx)FeAs.Europhys Lett 2008; 83: 27006.

[68] Uemura, YJ. Commonalities in phase and mode. NatMater 2009; 8, 253.

[69] Scalapino, DJ. A common thread: The pairing interac-tion for unconventional superconductors. Rev Mod Phys2012; 84: 1383.

[70] Kim, MG, Kreyssig, A and Lee, YB et al. Commensu-rate antiferromagnetic ordering in Ba(Fe1−xCox )2As2determined by x-ray resonant magnetic scattering at theFe K edge. Phys Rev B 2010; 82: 180412(R).

[71] Wang, MY, Luo, HQ and Zhao, J et al. Electron-dopingevolution of the low-energy spin excitations in the ironarsenide superconductor BaFe2−xNixAs2. Phys Rev B2010; 81: 174524.

[72] Wang, MY, Luo, HQ and Wang, M et al. Magnetic fieldeffect on static antiferromagnetic order and spin exci-tations in the underdoped iron arsenide superconductorBaFe1.92Ni0.08As2. Phys Rev B 2011; 83: 094516.

[73] Nandi, S, Kim, MG and Kreyssig, A el al. Anoma-lous Suppression of the Orthorhombic Lattice Distortionin Superconducting Ba(Fe1−xCox)2As2 Single Crystals.Phys Rev Lett 2010; 104: 057006.

[74] Pratt, DK, Kim, MG and Kreyssig, A et al. Incom-mensurate Spin-Density Wave Order in Electron-DopedBaFe2As2 Superconductors. Phys Rev Lett 2011; 106:257001.

[75] Luo, HQ, Zhang, R and Laver, M et al. Coexistence andCompetition of the Short-Range Incommensurate Anti-ferromagnetic Order with the Superconducting State ofBaFe2−xNixAs2. Phys Rev Lett 2012; 108: 247002.

[76] Lu, XY, Gretarsson, H and Zhang, R et al.AvoidedQuantum Criticality and Magnetoelastic Coupling inBaFe2−xNixAs2. Phys Rev Lett 2013; 110: 257001.

[77] Avci, S, Chmaissem, O and Chung, DY et al. Phase dia-gram of Ba1−xKxFe2As2. Phys Rev B 2012; 85: 184507.

[78] Li, L, Luo,Y and Wang, QB et al. Superconductivityinduced by Ni doping in BaFeh2Ash2 single crystals.New J Phys 2009; 11: 025008.

[79] Rotter, M, Pangerl, M and Tegel, M et al. Superconduc-tivity and crystal structures of (Bah1−xKhx)Feh2ASh2

(x=0-1). Angew Chem Int Ed 2008; 47: 7949.

22

[80] Harriger, LW, Luo, HQ and Liu, MS et al. Nematic spinfluid in the tetragonal phase of BaFeh2Ash2. Phys RevB 2011; 84: 054544.

[81] Liu, MS, Harriger, LW and Luo, HQ et al.Nature of magnetic excitations in superconductingBaFeh1.9Nih0.1Ash2. Nat Phys 2012; 8: 376.

[82] Luo, HQ, Lu, XY and Zhang, R et al. Elec-tron doping evolution of the magnetic excitations inBaFeh2−xNihxAsh2. Phys Rev B 2013; 88: 144516.

[83] Wang, M, Zhang, CL and Lu, XY et al. Doping de-pendence of spin excitations and its correlations withhigh-temperature superconductivity in iron pnictides.Nat Commun 2013; 4: 2874.

[84] Zhang, CL, Wang, M and Luo, HQ et al. NeutronScattering Studies of spin excitations in hole-dopedBah0.67Kh0.33Feh2Ash2 superconductor. Sci Rep 2011;1: 115.

[85] Castellan,JP, Rosenkranz, S and Goremychkin, EA etal. Effect of Fermi Surface Nesting on Resonant Spin Ex-citations in Bah1−xKhxFeh2Ash2. Phys Rev Lett 2011;107: 177003.

[86] Lee, CH, Kihou, K and Kawano-Furukawa, H et al.Incommensurate Spin Fluctuations in Hole-OverdopedSuperconductor KFe2As2. Phys Rev Lett 2011; 106:067003.

[87] Zhao, J, Adroja, DT and Yao, DX et al. Spin wavesand magnetic exchange interactions in CaFeh2Ash2. NatPhys 2009; 5: 555.

[88] Christianson, AD, Goremychkin, EA and Osborn,R et al. Unconventional superconductivity inBah0.6Kh0.4Feh2Ash2 from inelastic neutron scat-tering. Nature 2008; 456: 930.

[89] Lumsden, MD, Christianson, AD and Parshall, Det al. Two-dimensional resonant magnetic excitationin BaFeh1.84Coh0.16Ash2. Phys Rev Lett 2009; 102:107005.

[90] Chi SX, Schneidewind, A and Zhao, J et al. In-elastic Neutron-Scattering Measurements of a Three-Dimensional Spin Resonance in the FeAs-BasedBaFeh1.9Nih0.1Ash2 Superconductor. Phys Rev Lett2009; 102: 107006.

[91] Li, SL, Chen, Y and Chang, S et al. Spin gap and mag-netic resonance in superconducting BaFe1.9Ni0.1As2.Phys Rev B 2009; 79: 174527.

[92] Eschrig, M. The effect of collective spin-1 excitationson electronic spectra in high-T-c superconductors. AdvPhys 2006; 55: 47.

[93] Park, JT, Inosov, DS and Yaresko, A et al. Symmetry ofspin excitation spectra in the tetragonal paramagneticand superconducting phases of 122-ferropnictides. PhysRev B 2010; 82 : 134503.

[94] Zhou, KJ, Huang, YB and Monney C et al. Persistenthigh-energy spin excitations in iron-pnictide supercon-ductors. Nature Communications 2013; 4: 1470.

[95] Lester, C, Chu, JH and Analytis, JG et al. Dispersivespin fluctuations in the nearly optimally doped super-conductor Ba(Fe1−xCox)2As2 (x=0.065). Phys Rev B2010; 81 : 064505.

[96] Bardeen, J, Cooper, LN and Schrieffer, JR. Theory ofSuperconductivity. Phys Rev 1957; 108: 1175-1204.

[97] Chester, GV. Difference between Normal and Supercon-ducting States of a Metal. Phys Rev 1956; 103: 1693-1699.

[98] See, for example, J. R. Schrieffer, Perseus books, 1999.

[99] Tranquada, JM, Xu, GY and Zaliznyak, IA. Supercon-ductivity, antiferromagnetism, and neutron scattering.J Magn Magn Mater 2014; 350: 148.

[100] Headings, NS, Hayden, SM and Coldea, R et al.Anomalous High-Energy Spin Excitations in the High-T-c Superconductor-Parent Antiferromagnet La2CuO4.Phys Rev Lett 2010; 105: 247001.

[101] Demler, E and Zhang, SC. Quantitative test of a micro-scopic mechanism of high-temperature superconductiv-ity. Nature 1998; 396: 733-735.

[102] Woo, H, Dai, PC and Hayden SM et al. Magnetic en-ergy change available to superconducting condensationin optimally doped YBa2Cu3O6.95. Nat Phys 2006; 2:600-604.

[103] Dahm, T, Hinkov, V and Borisenko, SV et al.Strengthof the spin-fluctuation-mediated pairing interaction ina high-temperature superconductor. Nat Phys 2009; 5:217-221.

[104] Stockert, O, Arndt, J and Faulhaber, E et al. Magnet-ically driven superconductivity in CeCu2Si2. Nat Phys2011; 7: 119-124.

[105] Ning, FL, Ahilan, K and Imai T et al. ContrastingSpin Dynamics between Underdoped and OverdopedBa(Fe1−xCox)2As2. Phys. Rev. Lett. 2010; 104: 037001.

[106] Soh, JH, Tucker, GS and Pratt, DK et al. InelasticNeutron Scattering Study of a Nonmagnetic CollapsedTetragonal Phase in Nonsuperconducting CaFe2As2:Evidence of the Impact of Spin Fluctuations on Su-perconductivity in the Iron-Arsenide Compounds. Phys.Rev. Lett. 2013; 111: 227002.

[107] Ma, FJ and Lu, ZY. Iron-based layered compoundLaFeAsO is an antiferromagnetic semimetal. Phys RevB 2008; 78: 033111.

[108] Yang, LX, Zhang, Y and Ou, HW et al ElectronicStructure and Unusual Exchange Splitting in the Spin-Density-Wave State of the BaFe2As2 Parent Com-pound of Iron-Based Superconductors. Phys Rev Lett2009; 102: 107002.

[109] Yang, LX, Xie, BP and Zhang, Y et al. Surface andbulk electronic structures of LaFeAsO studied by angle-resolved photoemission spectroscopy. Phys Rev B 2010;82: 104519.

[110] He, C, Zhang, Y, and Xie, BP et al. Electronic-Structure-Driven Magnetic and Structure Transitions inSuperconducting NaFeAs Single Crystals Measured byAngle-Resolved Photoemission Spectroscopy. Phys RevLett 2010; 105: 117002.

[111] Zhang, Y, Chen, F and He, C et al. Strong correlationsand spin-density-wave phase induced by a massive spec-tral weight redistribution in α− Fe1.06Te. Phys Rev B2010; 82: 165113.

[112] Chen, F, Zhou, B and Zhang, Y et al. Electronicstructure of Fe1.04Te0.66Se0.34. Phys Rev B 2010; 81:014526.

[113] Zhao, L, Mou, DX and Liu, SY et al. Common Fermi-surface topology and nodeless superconducting gap ofK0.68Fe1.79Se2 and (T l0.45K0.34)Fe1.84Se2 supercon-ductors revealed via angle-resolved photoemission. PhysRev B 2011; 83: 140508(R).

[114] Zhang, Y, Yang, LX and Xu, M et al. Nodeless super-conducting gap in AxFe2Se2(A = K,Cs) revealed byangle-resolved photoemission spectroscopy. Nat Mater2011; 10: 273.

23

[115] Tan, SY, Zhang, Y and Xia, M et al. Interface-inducedsuperconductivity and strain-dependent spin densitywaves in FeSe/SrT iO3 thin films. Nat Mater 2013; 12:634.

[116] Ye, ZR, Zhang, Y and Xu, M et al. Orbital selectivecorrelations between nesting/scattering/Lifshitz transi-tion and the superconductivity in AFe1−xCoxAs(A =Li,Na). arXiv 2013; 1303.0682.

[117] Singh, DJ. Electronic structure of Fe-based supercon-ductors. Physica C 2009; 469: 418.

[118] Zhang, Y, Chen, F and He, C et al. Orbital char-acters of bands in the iron-based superconductorBaFe1.85Co0.15As2. Phys Rev B 2011; 83: 054510.

[119] Mazin, II and Schmalian, J. Pairing symmetry and pair-ing state in ferropnictides: Theoretical overview. Phys-ica C 2009; 469: 614.

[120] Ye, ZR, Zhang, Y and Chen, F et al. Doping depen-dence of the electronic structure in phosphorus-dopedferropnictide superconductor BaFe2(As1−xPx)2 stud-ied by angle-resolved photoemission spectroscopy. PhysRev B 2012; 86: 035136.

[121] Sato, T, Nakayama, K and Sekiba, Y et al. Band Struc-ture and Fermi Surface of an Extremely OverdopedIron-Based Superconductor KFe2As2. Phys Rev Lett2009; 101: 047002.

[122] Dhaka, RS, Liu, C and Fernandes, RM et al. WhatControls the Phase Diagram and Superconductivity inRu-Substituted BaFe2As2. Phys Rev Lett 2011; 107:267002.

[123] Ishida, S, Nakajima, M and Liang, T et al.Anisotropy of the In-Plane Resistivity of UnderdopedBa(Fe1−xCox)2As2 Superconductors Induced by Impu-rity Scattering in the Antiferromagnetic OrthorhombicPhase. Phys Rev Lett 2013; 110: 207001.

[124] Zhang, Y, Ye, ZR and Ge, QQ et al. Nodalsuperconducting-gap structure in ferropnictide super-conductor BaFe2(As0.7P0.3)2. Nat Phys 2012; 8: 371.

[125] Chu, JH, Analytis, JG and Greve, KD et al. In-PlaneResistivity Anisotropy in an Underdoped Iron ArsenideSuperconductor. Science 2010; 329: 824.

[126] Shimojima, T, Sakaguchi, F and Ishizaka, K et al.Orbital-Independent Superconducting Gaps in IronPnictides. Science 2011; 332: 564.

[127] Lee, CC, Yin, WG and Ku, W. Ferro-Orbital Order andStrong Magnetic Anisotropy in the Parent Compoundsof Iron-Pnictide Superconductors. Phys Rev Lett 2009;103: 267001.

[128] Chuang, TM, Allan, MP and Lee, JH et al. Ne-matic Electronic Structure in the “Parent” State of theIron-Based Superconductor Ca(Fe1−xCox)2As2. Sci-ence 2010; 327: 181.

[129] Zhang, Y, He, C and Ye, ZR et al. Symmetry break-ing via orbital-dependent reconstruction of electronicstructure in detwinned NaFeAs. Phys Rev B 2012; 85:085121.

[130] Yi, M, Lu, DH and Chu, JH et al. Symmetry-breaking orbital anisotropy observed for detwinnedBa(Fe1−xCox)2As2 above the spin density wave tran-sition. Proc Natl Acad Sci 2011; 108: 6878.

[131] Hu, JP and Xu, CK. Nematic orders in Iron-based su-perconductors. arXiv 2011; 1112.2713.

[132] Bao, W, Qiu, Y and Huang, Q et al. Tunable (δπ, δπ)-Type Antiferromagnetic Order in α−Fe(Te, Se) Super-conductors. Phys Rev Lett 2009; 102: 247001.

[133] Ma, FJ, Ji, W and Hu, JP et al. First-PrinciplesCalculations of the Electronic Structure of Tetragonalα − FeTe and α − FeSe Crystals: Evidence for a Bi-collinear Antiferromagnetic Order. Phys Rev Lett 2009;102: 177003.

[134] Li, SL, Cruz, Cdl and Huang, Q et al. First-order magnetic and structural phase transitions inFe1+ySexTe1−x. Phys Rev B 2009; 79: 054503.

[135] Ding, H, Richard, P and Nakayama, K et al. Observa-tion of Fermi-surface-dependent nodeless superconduct-ing gaps in Ba0.6K0.4Fe2As2. Europhys Lett 2008; 83:47001.

[136] Terashima, K, Sekiba, Y and Bowen, JH et al. Fermisurface nesting induced strong pairing in iron-based su-perconductors. Proc Natl Acad Sci 2009; 106: 7330.

[137] Miao, H, Richard, P and Tanaka Y et al. Isotropic su-perconducting gaps with enhanced pairing on electronFermi surfaces in FeTe0.55Se0.45. Phys Rev B 2012; 85:094506.

[138] Hashimoto, K, Yamashita, M and Kasahara, S etal. Line nodes in the energy gap of superconductingBaFe2(As1−xPx)2 single crystals as seen via penetra-tion depth and thermal conductivity. Phys Rev B 2010;81: 220501.

[139] Yamashita, M, Senshu, Y and Shibauchi, T et al. Nodalgap structure of superconducting BaFe2(As1−xPx)2from angle-resolved thermal conductivity in a magneticfield. Phys Rev B 2011; 84: 060507.

[140] Nakai, Y, Iye, T and Kitagawa, S et al. 31P and 75AsNMR evidence for a residual density of states at zeroenergy in superconducting BaFe2(As0.67P0.33)2. PhysRev B 2010; 81: 020503(R).

[141] Hashimoto, K, Kasahara, S and Katsumata, R et al.Nodal versus Nodeless Behaviors of the Order Param-eters of LiFeP and LiFeAs Superconductors from Mag-netic Penetration-Depth Measurements. Phys Rev Lett2012; 108: 047003.

[142] Qiu, X, Zhou, SY and Zhang, H et al. RobustNodal Superconductivity Induced by Isovalent Dopingin Ba(Fe1−xRux)2As2 and BaFe2(As1−xPx)2. PhysRev X 2012; 2: 011010.

[143] Dong, JK, Zhou, SY and Guan, TY et al. QuantumCriticality and Nodal Superconductivity in the FeAs-Based Superconductor KFe2As2. Phys Rev Lett 2010;104: 087005.

[144] Song, CL, Wang, YL and Cheng, P et al. Direct Obser-vation of Nodes and Twofold Symmetry in FeSe Super-conductor. Science 2011; 332: 1410.

[145] Dong, JK, Zhou, SY and Guan, TY et al. Thermal con-ductivity of overdoped BaFe1.73Co0.27As2 single crys-tal: Evidence for nodeless multiple superconductinggaps and interband interactions. Phys Rev B 2010; 81:094520.

[146] Khasanov, R, Conder, K and Pomjakushina, E et al. Ev-idence of nodeless superconductivity in FeSe0.85 from amuon-spin-rotation study of the in-plane magnetic pen-etration depth. Phys Rev B 2008; 78: 220510.

[147] Chi, S, Grothe, S and Liang, RX et al. Scanning Tun-neling Spectroscopy of Superconducting LiFeAs SingleCrystals: Evidence for Two Nodeless Energy Gaps andCoupling to a Bosonic Mode. Phys Rev Lett 2012; 109:087002.

[148] Ding, L, Dong, JK and Zhou, SY et al. Nodeless su-perconducting gap in electron-doped BaFe1.9Ni0.1As2

24

probed by quasiparticle heat transport. New J Phys2009; 11: 093018.

[149] Zhang, Y, Yang, LX and Chen, F et al. Out-of-Plane Momentum and Symmetry-Dependent EnergyGap of the Pnictide Ba0.6K0.4Fe2As2 Superconduc-tor Revealed by Angle-Resolved Photoemission Spec-troscopy. Phys Rev Lett 2010; 105: 117003.

[150] Kuroki, K, Onari, S and Arita, R et al. Unconven-tional Pairing Originating from the Disconnected FermiSurfaces of Superconducting LaFeAsO1−xFx. Phys RevLett 2008; 101: 087004.

[151] Mazin, II, Singh, DJ and Johannes, MD et al. Un-conventional Superconductivity with a Sign Reversal inthe Order Parameter of LaFeAsO1−xFx. Phys Rev Lett2008; 101: 057003.

[152] Hanaguri, T, Niitaka, S and Kuroki, K et al. Unconven-tional s-Wave Superconductivity in Fe(Se,Te). Science2010; 328: 474.

[153] Suzuki, K, Usui, H and Kuroki, K. Possible Three-Dimensional Nodes in the s± Superconducting Gap ofBaFe2(As1−xPx)2. J Phys Soc Jpn 2011; 80: 013710.

[154] Okazaki, K, Ota, Y and Kotani, Y et al. Octet-LineNode Structure of Superconducting Order Parameter inKFe2As2. Science 2012; 337: 1314.

[155] Xu, N, Richard, P and Shi, X et al. Possible nodalsuperconducting gap and Lifshitz transition in heav-ily hole-doped Ba0.1K0.9Fe2As2. Phys Rev B 2013; 88:220508(R).

[156] Drew, AJ, Niedermayer, C and Baker, PJ et al. Co-existence of static magnetism and superconductivity inSmFeAsO1−xFx as revealed by muon spin rotation. NatMater 2009; 8: 310.

[157] Fernandes, RM, Pratt, DK and Tian, W et al. Uncon-ventional pairing in the iron arsenide superconductors.Phys. Rev. B 2010; 81: 140501.

[158] Chen, H, Ren, Y and Qiu, Y. et al. Coexistenceof the spin-density wave and superconductivity inBa1−xKxFe2As2. Europhys. Lett. 2009; 85: 17006.

[159] Ge, QQ, Ye, ZR and Xu, M et al. Anisotropic butNodeless Superconducting Gap in the Presence ofSpin-Density Wave in Iron-Pnictide SuperconductorNaFe1−xCoxAs. Phys Rev X 2013; 3: 011020.

[160] Zhang, Y, Wei, J and Ou, HW et al. Unusual Dop-ing Dependence of the Electronic Structure and Coexis-tence of Spin-Density-Wave and Superconductor Phasesin Single Crystalline Sr1−xKxFe2As2. Phys Rev Lett2009; 102: 127003.

[161] Cai, P, Zhou, XD and Ruan, W et al. Visualizing the mi-croscopic coexistence of spin density wave and supercon-ductivity in underdoped NaFe1−xCoxAs. Nature Com-munication 2013; 4: 1596.

[162] Parker, D, Vavilov, MG and Chubukov AV et al. Co-existence of superconductivity and a spin-density wavein pnictide superconductors: Gap symmetry and nodallines. Phys Rev B 2009; 80: 100508(R).

[163] S. Maiti, R. M. Fernandes and A. V. Chubukov, Gapnodes induced by coexistence with antiferromagnetismin iron-based superconductors. Phys Rev B 2012; 85:144527.

[164] Liu, C, Palczewski, AD and Dhaka, RS et al. Im-portance of the Fermi-surface topology to the su-perconducting state of the electron-doped pnictideBa(Fe1−xCox)2As2. Phys Rev B 2011; 84: 020509(R).

[165] Shen, XP, Chen, SD and Ge QQ et al. Electronicstructure of Ca10(Pt4As8)(Fe2−xPtxAs2)5 with metal-lic Pt4As8 layers: An angle-resolved photoemissionspectroscopy study. Phys Rev B 2013; 88: 115124.

[166] Li, J, Guo, YF and Zhang, SB et al. Superconductivitysuppression of Ba0.5K0.5Fe2−2xM2xAs2 single crystalsby substitution of transition metal (M = Mn, Ru, Co,Ni, Cu, and Zn). Phys Rev B 2012; 85: 214509.

[167] Suzuki, H, Yoshida, T and Ideta, S et al. Absenceof superconductivity in the hole-doped Fe pnictideBa(Fe1−xMnx)2As2: Photoemission and x-ray ab-sorption spectroscopy studies. Phys Rev B 2013; 88:100501(R).

[168] Hu, JP, and Ding, H. Local antiferromagnetic exchangeand collaborative Fermi surface as key ingredients ofhigh temperature superconductors. Scientific Reports2012; 2: 381.

[169] He, SL, He, JF and Zhang, WH et al. Phase diagramand electronic indication of high-temperature supercon-ductivity at 65 K in single-layer FeSe films. Nat Mater2013; 12: 605.

[170] Chen, F, Xu, M and Ge, QQ et al. Electronic Identi-fication of the Parental Phases and Mesoscopic PhaseSeparation of KxFe2−ySe2 Superconductors. Phys RevX 2011; 1: 021020.

[171] Li, W and Ding, H and Deng, P et al. Phase separationand magnetic order in K-doped iron selenide supercon-ductor. Nat Phys 2012; 8: 126.

[172] Wang, Z, Song, YJ and Shi, HL et al. Microstructureand ordering of iron vacancies in the superconductorsystem KyFexSe2 as seen via transmission electron mi-croscopy. Phys Rev B 2011; 83: 140505(R).

[173] Xu, M, Ge, QQ and Peng, R et al. Evidence for an s-wave superconducting gap in KxFe2−ySe2 from angle-resolved photoemission. Phys Rev B 2012; 85: 220504.

[174] Park, JT, Friemel, G and Li Y et al. Magnetic ResonantMode in the Low-Energy Spin-Excitation Spectrum ofSuperconducting Rb2Fe4Se5 Single Crystals. Phys RevLett 2011; 107: 177005.177005.

[175] Peng, R, Shen, XP and Xie, X et al. Enhanced supercon-ductivity and evidence for novel pairing in single-layerFeSe on SrT iO3 thin film under large tensile strain.arXiv 2013; 1310.3060.

[176] Hu, JP. Iron-Based Superconductors as Odd-Parity Su-perconductors. Phys Rev X 2013; 3: 031004.

[177] Peng, R, Xu, HC and Tan, SY et al. Critical role of sub-strate in the high temperature superconductivity of sin-gle layer FeSe on Nb : BaTiO3. arXiv 2014; 1402.1357.

[178] Yin, WG, Lee, CC and Ku, W Unified Picture for Mag-netic Correlations in Iron-Based Superconductors. PhysRev Lett 2010; 105: 107004.

[179] Yin, ZP, Haule, K and Kotliar, G Kinetic frustrationand the nature of the magnetic and paramagnetic statesin iron pnictides and iron chalcogenides. Nat Mater2011; 10: 932.

[180] Jiang, J, He, C and Zhang, Y et al. Distinct in-planeresistivity anisotropy in a detwinned FeTe single crystal:Evidence for a Hund’s metal. Phys. Rev. B 2013; 88:115130.

[181] Kaneko, K, Hoser, A and Caroca-Canales, N et al.Columnar magnetic structure coupled with orthorhom-bic distortion in the antiferromagnetic iron arsenideSrFe2As2. Phys Rev B 2008; 78: 212502.

25

[182] Xiao, Y, Su, Y and Meven, M et al. Magnetic struc-ture of EuFe2As2 determined by single-crystal neutrondiffraction. Phys Rev B 2009; 80: 174424.

[183] Goldman, AI, Argyriou, DN and Ouladdiaf, B et al. Lat-tice and magnetic instabilities in CaFe2As2: A single-crystal neutron diffraction study. Phys Rev B 2008; 78:100506.

[184] Chen, Y, Lynn, JW and Li, J et al. Magnetic orderof the iron spins in NdFeAsO. Phys Rev B 2008; 78:064515.

[185] Wilson, SD, Yamani, Z and Rotundu, CR et al. Neutrondiffraction study of the magnetic and structural phasetransitions in BaFe2As2. Phys Rev B 2009; 79: 184519.

[186] Zhao, J, Huang, Q and Cruz, DL et al. Lattice andmagnetic structures of PrFeAsO, PrFeAsO0.85F0.15,and PrFeAsO0.85. Phys Rev B 2008; 78: 132504.

[187] Lester, C, Chu, JH and Analytis, JG et al. Neutronscattering study of the interplay between structure andmagnetism in Ba(Fe1−xCox)2As2. Phys Rev B 2009;79: 144523.

[188] Park, JT, Inosov, DS and Niedermayer, C et al. Elec-tronic Phase Separation in the Slightly Underdoped IronPnictide Superconductor Ba1−xKxFe2As2. Phys RevLett 2009; 102: 117006.

[189] Li, SL, Cruz, CDL and Huang, Q et al. Structural andmagnetic phase transitions in Na1−δFeAs. Phys Rev B2009; 80: 020504.

[190] Lee, JJ, Schmitt, FT and Moore, RG et al. Evidence forpairing enhancement in single unit cell FeSe on SrT iO3

due to cross-interfacial electron-phonon coupling. arXiv2014; 1312.2633.

[191] McMillan, WL. Transition Temperature of Strong-Coupled Superconductors. Phys Rev 1968; 167: 331.

[192] Ma, F, Lu, ZY and Xiang, T. Main Interactions in Iron-based Superconductors. Front. Phys. China 2010; 5:150.

[193] Yildirim, T. Origin of the 150-K Anomaly in LaFeAsO:Competing Antiferromagnetic Interactions, Frustration,and a Structural Phase Transition. Phys. Rev. Lett.2008; 101: 057010.

[194] Ma, F, Lu, ZY and Xiang, T. Arsenic-bridged antiferro-magnetic superexchange interactions in LaFeAsO. Phys.Rev. B 2008; 78: 224517.

[195] Liu, K, Lu, ZY and Xiang T. Atomic and electronicstructures of FeSe monolayer and bilayer thin filmson SrTiO3 (001): First-principles study. Phys. Rev. B2012; 85: 235123.

[196] Liu, D, Zhang, WH and Mou, DX et al. Electronicorigin of high-temperature superconductivity in single-layer FeSe superconductor. Nature Commun. 2012; 3:931.

[197] Bao, W, Huang, QZ and Chen, GF et al. A Novel LargeMoment Antiferromagnetic Order in K0.8Fe1.6Se2 Su-perconductor. Chin. Phys. Lett. 2011; 28: 086104.

[198] Kou, SP, Li, T, and Weng, ZY. Coupled Local Momentsand Itinerant Electrons in Iron-Based Superconductors.Europhys Lett 2009; 88: 17010.

[199] Si, Q and Abrahams, E, Strong Correlations and Mag-netic Frustration in the High Tc Iron Pnictides. Phys.

Rev. Lett. 2008; 101: 076401.[200] Seo, K, Bernevig, BA and Hu, J. Pairing Symmetry in

a Two-Orbital Exchange Coupling Model of Oxypnic-tides. Phys. Rev. Lett. 2008; 101: 206404.

[201] Wang, F, Zhai, H and Ran, Y et al. FunctionalRenormalization-Group Study of the Pairing Symme-try and Pairing Mechanism of the FeAs-Based High-Temperature Superconductor. Phys. Rev. Lett. 2009:102: 047005.

[202] Kuroki, K, Usui, H and Onari, S et al. Pnictogen heightas a possible switch between high-Tc nodeless and low-Tc nodal pairings in the iron-based superconductors.Phys. Rev. B 2009; 79: 224511.

[203] Chen, WQ, Yang, KY and Zhou, Y et al. Strong Cou-pling Theory for Superconducting Iron Pnictides, PhysRev Lett 2009; 102: 047006.

[204] Onari, S and Kontani, H, Violation of Anderson’s theo-rem for the sign-reversing s-wave state of iron-pnictidesuperconductors. Phys. Rev. Lett. 2009; 103: 177001.

[205] Chen, WQ, Ma, FJ and Lu, ZY et al. π-Junction toProbe Antiphase s-Wave Pairing in Iron Pnictide Su-perconductors, Phys Rev Lett 2009; 103: 207001.

[206] Inosov, DS, Park, JT and Bourges, P et al.Normal-state spin dynamics and temperature-dependent spin-resonance energy in optimally dopedBaFe1.85Co0.15As2. Nat. Phys. 2010; 6: 178.

[207] Li, S, Zhang, C and Wang, M et al. Normal-State Hour-glass Dispersion of the Spin Excitations in FeSexTe1−x.Phys. Rev. Lett. 2010; 105: 157002.

[208] Li, YK, Tong, J and Tao, Q et al. Effect of a Zn im-purity on Tc and its implications for pairing symmetryin LaFeAsO1−xFx, New Journal of Physics 2010; 12:083008.

[209] Fernandes, RM and Schmalian, J. Competing order andnature of the pairing state in the iron pnictides. Phys.Rev. B 2010; 82: 014521.

[210] Laplace, Y, Bobroff, J and Rullier-Albenque, Fet al. Atomic coexistence of superconductivity andincommensurate magnetic order in the pnictideBa(Fe1−xCox)2As2. Phys. Rev. B 2009; 80: 140501.

[211] Zhang, Y and Feng, DL. Angle-Resolved Photoemis-sion Spectroscopy Study on Iron-Based Superconduc-tors. AAPPS Bulletin 2012; 22: 2.

[212] Ye, ZR, Zhang, Y, Xie, BP and Feng, DL. Angle-resolved photoemission spectroscopy study on iron-based superconductors. Chinese Physics B 2013; 22:087407.

[213] Umezawa, K, Li, Y and Miao, H et al. Unconven-tional Anisotropic s-Wave Superconducting Gaps of theLiFeAs Iron-Pnictide Superconductor. Phys. Rev. Lett.2012; 108: 037002.

[214] Medvedev, S, MacQueen, TM and Troyan, IA et al.Electronic and magnetic phase diagram of β-Fe1.01Sewith superconductivity at 36.7 K under pressure. NatMater 2009; 8: 630.