ambient-pressure high-temperature superconductivity in...
TRANSCRIPT
PAPER • OPEN ACCESS
Ambient-pressure high-temperature superconductivity in stoichiometrichydrogen-free covalent compound BSiC2
To cite this article: Peng-Jen Chen and Horng-Tay Jeng 2020 New J. Phys. 22 033046
View the article online for updates and enhancements.
This content was downloaded from IP address 140.114.63.4 on 26/03/2020 at 02:36
New J. Phys. 22 (2020) 033046 https://doi.org/10.1088/1367-2630/ab76ad
PAPER
Ambient-pressure high-temperature superconductivity instoichiometric hydrogen-free covalent compound BSiC2Peng-JenChen1,2,3,4,7 andHorng-Tay Jeng1,5,6,7
1 Institute of Physics, Academia Sinica, Taipei 11529, Taiwan2 Institute of Atomic andMolecular Sciences, Academia Sinica, Taipei 10617, Taiwan3 Department of Physics, National TaiwanUniversity, Taipei 10617, Taiwan4 Nano Science andTechnology Program, Taiwan International Graduate Program,Academia Sinica, Taipei 11529, Taiwan andNational
TaiwanUniversity, Taipei 10617, Taiwan5 Department of Physics, National TsingHuaUniversity, Hsinchu 30013, Taiwan6 PhysicsDivision, National Center for Theoretical Sciences, Hsinchu 30013, Taiwan7 Authors towhomany correspondence should be addressed.
E-mail: [email protected] and [email protected]
Keywords: superconductingmaterials,metallic covalentmaterials, first-principles calculations
Supplementarymaterial for this article is available online
AbstractHigh superconducting critical temperature (Tc) of 73.6 K at ambient pressure is predicted in BSiC2 bymeans of the first-principles electron–phonon calculations.Without the need for doping orpressurization, the stoichiometric BSiC2 exhibits strong electron–phonon coupling (EPC) and highestTc amongBCS-superconductors at ambient pressure. Also, it is hydrogen-free thatmakes easier thesample growth. The dramatic softening of the E g2 mode is themain account for the strong EPC. Inaddition, we find that BC3, derived from the replacement of Si in BSiC2 by another C, is alsosuperconductingwith a highTc ∼ 40 K.Ourwork indicates that thesematerials form anew family ofhigh-Tc BCS-superconductors at ambient pressure.
1. Introduction
Superconductivity is one of themost intriguing phenomena inmaterials science. Searching for newsuperconductors that exhibit highTc is of equal importance. Superconductors can be classified into various typesaccording to the pairingmechanism, and the ones that exhibit highestTc within each class are the following. Forcuprates, the highestTc at ambient pressure is observed inHgBaCaCuO (∼ 135 K) [1], which is also the one thatexhibits highestTc among all types of superconductors at ambient pressure.Many other cuprates also exhibit
>T 100c K. Recently, iron-based superconductors are found to showhighTc [2]. The highestTc ∼ 55 K is foundin doped SmFeAsO [3, 4]. An even higherTc is reportedwhen depositing a single layer FeSe on SrTiO3 [5, 6].Although the pairingmechanism is not yet fully understood, it is believed that the antiferromagnetic spin-fluctuationsmight be responsible for the pairing in iron-based superconductors [7]. For BCS-superconductors,it is experimentally demonstrated very recently that the lanthanumhydride (LaH10) exhibits superconductivityat temperatures close to 260 Kunder extremely high pressure [8]. At ambient pressure,MgB2 exhibits thehighestTc (∼39 K) [9] among all BCS-superconductors.MgB2 consists of hexagonal B2 layers intercalatedwithMg2+ ions,making it isoelectronic to graphite with two-dimensional s- and three-dimensional (3D) p-bandsformed by the sp2 and pz orbitals, respectively. It has been shown bymeans of various techniques [10–17] thatthere are two distinct superconducting gaps resulted from the s- and p- bands at the Fermi level. Aphenomenological two-gapmodel has also been proposed to explain the observed specific heat ofMgB2 [18]. Onthe theoretical side, the two-gap nature is clearly demonstrated [19–23] and successfully explainsmanysuperconducting properties ofMgB2. It is also essential tomention that themetallization of the s-bands, via theeffective hole-doping, is themain account for the superconductivity.
OPEN ACCESS
RECEIVED
19 September 2019
REVISED
6 February 2020
ACCEPTED FOR PUBLICATION
14 February 2020
PUBLISHED
25March 2020
Original content from thisworkmay be used underthe terms of the CreativeCommonsAttribution 4.0licence.
Any further distribution ofthis workmustmaintainattribution to theauthor(s) and the title ofthework, journal citationandDOI.
© 2020TheAuthor(s). Published by IOPPublishing Ltd on behalf of the Institute of Physics andDeutsche PhysikalischeGesellschaft
Since the discovery of the highTc inMgB2, there have been several works that theoretically propose possibleBCS-superconductors with highTc due to the hole-doped s-bands. For instance, CaB2, isostructural toMgB2,has been predicted to have aTc of∼ 55 K [24]. However, it ismetastable andmay easily formCaB6 andCaclusters during the synthesis process [25]. Optimally hole-doped LiBC [26, 27] could be superconductingwith
~T 100c K.Unfortunately, it is reported that heavily hole-doped LiBC causes severe shrinkage of the crystal[28–32], making the calculations based on the rigid shift of the Fermi level (virtual crystal approximation, VCA)invalid. Some Li-intercalated layered borocarbides are reported to become superconductors at 17–54 K,depending on the effective hole-doping level fromLi intercalation [33, 34]. These numerical results of Li-intercalated borocarbides do not suffer from theVCAproblem and hence the predictedTc might be reliable oncesuccessfully synthesized. Graphane [35] is theoretically claimed to exhibit superconductivity below∼ 100 Kwhen hole-doped [36]. It is interesting to note that graphane has no p-bands due to the passivation of hydrogenatoms.Nevertheless, pure graphane, i.e. the fully hydrogenated graphene, has not been successfully synthesizedup to now. Similarly, towhat extent will the dopants distort the structure and then disrupt the electron–phononcoupling (EPC) calculatedwithVCAusing the pristine crystal remains a question.Noteworthy tomention, highTc has also been predicted in dense carbon-basedmaterial: sodaliteNaC6 [37]. Different from the above-mentionedmaterials, the s-bands of sodaliteNaC6 are effectively electron-doped. Besides, the stability of thissuperconducting phasemay need further confirmation8.
Recently, highTc superconductivity in LaH10 (~260 K) andH3S (∼200 K) under extremely high pressurehas been theoretically predicted [38, 39] and then experimentally realized [8, 40]. Soon after, several hydrides arealso predicted to reveal superconductivity under high pressure [41–43]. These findings indicate the BCS-typesuperconductors can achieve quite highT .c Nonetheless, despite the excitement in the near realization of roomtemperature superconductivity, the required extremely high pressure prohibits further applications.Furthermore, the control of hydrogen during the sample growth is always an issue that needs careful treatment.Therefore, it is desirable tofind a stoichiometric hydrogen-freematerial that shows highTc at ambient pressure.
Except forNaC6, the aforementioned predicted superconductors, not yet realized though, have somecommon features. First, they crystallize in honeycomb structure. Second, the s-bands that consist of the orbitalsof the honeycomb constituents cross the Fermi level due to (effective) hole-doping; in other words, they aremetallic covalent compounds. Third, light atoms are involved in the E g2 or E g2 -like (referred to as E g2 hereafterfor brevity)mode that couples strongly to the s-bands. Following this direction, we start from a semiconductor,2H–SiC, and effectively hole-dope it by replacing half of Si by B.Wefind by first-principles scheme that thepristine BXC2 (X=Si andC) are superconductors with ¢T sc being about 74 K and 40 K for BSiC2 andBC3,respectively, based on the (Allen–Dynes–)McMillan formula. It is noted that our predictedTc in BC3 is close tothat of its cubic isomer at optimal doping [44]. Further investigation reveals unusual effect of the strong EPC inBSiC2. Generally, strong EPC is accompanied by dramatic band splitting owing to the corresponding largedeformation potential. For example, the s-bands inMgB2 are split by about 1.5 eV (with atomic displacementsof boron being~0.06 Å [20]) under the influence of the E g2 mode [19, 22]. Interestingly, the even stronger EPCin BSiC2 is not associatedwith severe splitting of the energy bands. This is because themain reason for the strongEPC in BSiC2 is the considerably softened E g2 mode and themoderate-to-strong phonon linewidth (PL). In BC3,on the contrary, softening of the E g2 mode is absent. The acoustic phonons, instead of the optical E g2 phonons asin BSiC2, play amore important role inmaking BC3 superconducting.
2. Computationalmethods
The electronic and electron–phonon calculations are performed usingQUANTUMESPRESSO (QE) code [45].Ultrasoft pseudopotentials with PBE functionals are used in all calculations. A ´ ´28 28 24 k-mesh and a
´ ´14 14 8 q-mesh are used in the electronic and phonon calculations. The energy cutoff of the planewaveexpansion is 50 Ry. The (electron-) phonon calculations are carried outwithin the framework of densityfunctional perturbation theory [46] implemented inQE. A smearing energy of 0.015 Ry is used to deal with thediscrete electronic states around the Fermi level in the calculations of PLs, and hence the EPC constant, l.
Having obtained the EPC strength, theTc can be estimated by using theMcMillan formula, with correctionsbyAllen andDynes [47]:
⎡⎣⎢
⎤⎦⎥
( )( )
( )w ll m l
= -+
- +T
1.20exp
1.04 1
1 0.62, 1c
ln
*
8While having obtained consistent crystal and band structures of the sodaliteNaC6, our phonon calculation indicates dynamical instability
that disagrees with the results shown in [37].
2
New J. Phys. 22 (2020) 033046 P-J Chen andH-T Jeng
or
⎡⎣⎢
⎤⎦⎥
( )( )
( )w l
l m l= -
+- +
Tf f
1.20exp
1.04 1
1 0.622c
1 2 ln
*
when l 1.5where
⎡⎣⎢
⎤⎦⎥
( ) ( ) ( )òwl
www
a w= Fexp2
dln
, 3ln2
( ) ( ) ( )òa w wl w d w w= -n n nF1
2d 4q q q
2
BZ
are the logarithmic average frequency and the isotropic Eliashberg spectral function, respectively, and
⎡
⎣⎢⎢
⎛⎝⎜
⎞⎠⎟
⎤
⎦⎥⎥ ( )l
= +L
f 1 , 511
32
13
⎛⎝⎜⎜
⎞⎠⎟⎟
( )
ww
l
l= +
á ñ-
+ Lf 1
1
62
2 12
ln
2
2 2
with the parameters L1 and L2 being
( ) ( )mL = +2.46 1 3.8 , 71 *
( ) ( )mww
L = + ´á ñ
1.82 1 6.3 . 82
2 12
ln
*
The EPC constant can be computed as:
( )å ål lp w
= =P
nn
n
n
nN9
q
q
qF2
with NF being the density of states at the Fermi level and P the PL. The screenedCoulombpotential m =* 0.1 isused in the estimation ofT .c
3. Results and discussion
3.1. Crystal and electronic structuresInherited from2H–SiC, the crystal structure of BSiC2 resembles that of the 2H–SiC, with the Si layers beingalternatively replaced by the B layers. Further replacement of the Si layers in BSiC2 byC layers leads to BC3. Thecrystal structures of bothmaterials are shown infigure 1. TheC atoms are labeled as C1 andC2, as well as C3 inBC3, infigure 1 to distinguish fromone another for they are electronically different. The relaxed latticeparameters are =a 2.89 Å, / =c a 1.66 for BSiC2 and =a 2.55 Å, / =c a 1.72 for BC3. Comparedwith=a 3.08 Å and / =c a 1.63 in 2H–SiC [48], the crystals of both BSiC2 andBC3 shrink because Si that has a
larger atomic radius is replaced. Owing to the common crystal structure and similar constituents, these twomaterials have similar band structure as shown infigure 2. Infigure 2(b) for BC3, there are three bands crossing
Figure 1. Side views of the crystal structure of (a)BSiC2 and (b)BC3. (c)The top viewof BSiC2 andBC3. The unit cell ismarked by thesolid lines. Yellow, blue, and green spheres represent the C, Si and B atoms, respectively. TheC atoms are further labeled as C1 andC2,as well as C3 in BC3, for their electronic difference. Color representations for the atoms are the same in all following figures. (d)Thehigh symmetry points in thefirst Brillouin zone.
3
New J. Phys. 22 (2020) 033046 P-J Chen andH-T Jeng
the Fermi level and the B-p orbitals contribute to the Fermi surfaces aswell. Rather than the formation of theexpected sp3 orbitals, the pxy and pz orbitals of C andB are almost decoupled; the hybridization happens betweenC-pxy andB-pxy orbitals and betweenC-pz andB-pz orbitals. The decoupling of in-plane and out-of-planecomponents of orbitals, whichmay take place in layeredmaterials where the crystal structure creates theanisotropy, is quietly rare in a 3Dmaterial. The Löwdin charges, ⟨ ∣ ⟩år y j= fn i i i n wherejn is the atomic
orbital and yi is the Kohn–Shamwave functionwhose occupancy is denoted by f ,i are 2.89, 3.93, 4.04, and 4.08for B, C1, C2, andC3 (the carbon that substitutes for the silicon in BSiC2). These results support the covalentbonding nature in BC3.While in BSiC2 as figure 2(a) displays, there arefive bands crossing the Fermi level. Fourof them are composed of theC-px,y orbitals (red and green bands) and the remaining one is from theC-pz orbital(blue band). The distinction between the twoC atoms can be seen by noting that the four s-bands crossing theFermi level form two groups. The two s-bands that are lower in energy come fromC2 and the other twomostlyfromC1. The overall C-pz components contribute to the pocket centering aroundΓ. The Löwdin charges of theC1, C2, B, and Si atoms are 4.75, 4.39, 2.90, and 2.86.While boron retainsmost of its valence electrons, siliconseems to donate one valence electron to carbon, acting electronically as a dopant; the covalency of the Si–Cbonds is reduced since one valence electron of silicon is donated to, rather than sharedwith, the neighboringcarbon. This is also evidenced by the partial density of states infigure 2(a) that the Si-p orbitals (orange line)contribute less to the valence bands than carbon. Similar with BC3, the C-px,y andC-pz orbitals barely hybridize.
The presence of such decoupling in a 3D covalentmaterial is bizarre andmay have profoundmeaning; itimplies that there exist two kinds of Fermi surface that are different and decoupled from each other, which canpossibly lead to two-gap superconductivity. This interesting property will be discussed later.We have alsoperformed structural search using universal structural predictor: evolutionary xtallography [49–51] and foundthat our predicted BSiC2 is the ground state of the hexagonal structures.
3.2. Phonons and superconductivityThe phonon spectra of BSiC2 andBC3, as well as the EPC strengths, are shown infigures 3(a) and (b). The E g2
and A g1 modes aremarked by the blue and green arrows, respectively. In BSiC2, the E g2 mode shows anextremely strong EPC (l =n 28.96q ) at phononwave vector /p=pq c (A point). Similar toMgB2, the E g2 modeshown infigure 3(c) couples strongly to theσ-bands that consist of C-px,y orbitals. The total EPC constantl = 2.41 yields a =T 73.6c K. (The commonly usedAllen–Dynes–McMillan formula (equation (1))yields∼ 58.8 K). It is noted that the E g2 mode is significantly softened as compared toMgB2 and othermaterialswith similar honeycomb structure [24, 26, 27, 33, 34, 36]. The softening of the E g2 mode plays a critical role inthe strong EPC in BSiC2 andwill be discussed later inmore detail. In BC3, however, the E g2 mode remains in thehigh energy region (∼ 80 meV). The resulting EPCof the E g2 mode ismuchweaker than that in BSiC2. Asfigure 3(b) reveals, the acoustic phononswith in-planemomenta are responsible for the occurrence ofsuperconductivity in BC3. The calculatedTc for BC3 is 39.3 Kwith l = 0.86.Wewould like tomention that thevalues ofTc and l of bothmaterials have little dependence on the smearing energy used to deal with the densityof states around the Fermi level, which indicates the numerical reliability of our results.
It is worthwhile to discuss the superconductivity inMgB2, BC3, andBSiC2 for comparison. Some propertiesof the E g2 mode related to superconductivity in the threematerials are listed in table 1. The EPC inMgB2originatesmainly from the interactions between the E g2 mode and the B-px,y electrons that form s-bondsbetween the B atoms. These electrons are well confinedwithin the two-dimensional boron sheets. Thus the EPCshows small qz-dependence, namely, the relative vibration (or phase) of the E g2 mode between different boron
Figure 2.Band structures and partial density of states (PDOS) of p-orbitals of (a)BSiC2 and (b)BC3. The color representations areshown in the top of the plots.
4
New J. Phys. 22 (2020) 033046 P-J Chen andH-T Jeng
sheets has negligible effect on the EPC. This is confirmed in ourwork (small variation of l listed in table 1) and ina previous work byKong et al [52]. Asmentioned previously, the s-bands are split by 1.5 eV due to the strongEPC resulting from the vibration of the E g2 mode [19, 22]. The stretch (compression) of the s-bonds inducesdepletion (aggregation) of charges.We refer to this as the intra-site orbital fluctuations under which theelectrons remain spatially confined between (or shared by) the bonded atoms. Intra-site orbital fluctuations dueto EPC commonly take place inmostmaterials, including BC3.
The influence of the E g2 mode on the orbitals of BSiC2 shows distinct behaviors, however. Figure 4 displaysthewave function of the highest occupied state at G. For the equilibrium structure as shown infigures 4(a) and(b), the charges center around the site of C2 atoms. This is consistent with the aforementioned littlehybridization between the Si–C p-orbitals. The out-of-phase frozen phonon ( /p=q c, i.e.A point, with largestdisplacement being 0.03 Å and increment in total energy per formula unit being 0.26 meV) induces strongspatial redistribution as depicted infigures 4(c) and (d). Notably, the band splitting is only∼0.2 eVwith thisdistortion (see supplementary information is available online at stacks.iop.org/NJP/22/033046/mmedia)despite its strong EPC (l = 23.91). It is apparent that a substantial weight of thewave function transfers toC1
and hybridizes with the B atoms, indicating inter-site orbitalfluctuations. The inter-site orbitalfluctuationsbring about the charge transfer fromC2 toC1 atoms.Wewould like to emphasize that the inter-site orbitalfluctuations take place in the highest occupied state at G and along G–A (see supplementary information),although only thewave function at G is shown infigure 4 for demonstration. For the Si–C2 bonds, however,there does not exist any phononmode that can give rise to hybridization. As a result, the charge densities aroundthe Si atoms remain low. This finding paves a newway of searching for newBCS-superconductors of highTc ifthe inter-site orbitalfluctuations are found to exist.
In comparisonwith the recently foundor proposed high-Tc BCS superconductors at highpressure, BSiC2 isadvantageous in two aspects. First, BSiC2 exhibits highTc at ambient pressure.Although interesting fromscientificpoint of view andpioneering in science advances, superconductivity existing at high pressure canhardly beused forfurther applications. Second, all these recently foundorproposed high-Tc BCS superconductors containhydrogen,which is difficult to control during the growth of crystals, especially under the condition of high pressure. Becausehydrogen is highly responsible for the strongEPC, superconductivitymay be suppressed if hydrogen atomsdonot
Figure 3.Phonon spectra and Eliashberg spectral function ( )a wF2 of (a)BSiC2 and (b)BC3. The size of the red dots represents themagnitude of the EPC l n.q Due to the extremely large l nq of the E2gmode aroundA in (a), we shrink the size of some dots by a factorof two and represent them in blue. The E2g andA1gmodes aremarked by the blue and green arrows, respectively. Note that the sizes ofthe dots in (a) and (b) are rescaled for visualization purpose, so the relative size of dots ismeaningful onlywithin each plot.Displacement pattern of theE2gmode that gives rise to the strong EPC inBSiC2 at q=A is shown in (c) for side (top panel) and top(bottompanel) views.
Table 1. Shown are theTc (Kelvin) obtained from isotropic Eliashberg equation, total EPCconstant, logarithmic average frequency w ln (Kelvin), the frequency w (meV), the associatedEPC constant l and the PL (GHz) of the E g2 mode atΓ andA in the three superconductors.
Tc Totalλ w ln /w wG A /l lAG PL (Γ/A)
MgB2 25.2a 0.70 728.5 66.88/60.10 2.79/2.08 2813/2107
BC3 39.3 0.86 728.1 81.57/81.17 0.91/0.18 1576/312
BSiC2 73.6 2.41 364.5 19.53/6.71 7.73/28.96 1323/584
a The experimental value of 39 K can be reproduced by taking into account the anisotropy in the
EPC and anharmonicity of theE2gmode [23, 53, 54].
5
New J. Phys. 22 (2020) 033046 P-J Chen andH-T Jeng
occupy the proper sites. Thehydrogen-free crystal structure prevents BSiC2 from this problem.As a result, wepropose thatBSiC2 is a promising high-Tc BCS superconductor in both fundamental studies and applications.
Nowwe are left with a question as towhy the E g2 mode in BSiC2 is significantly softened. Recall that the E g2
mode involves the compression of the B–C1 bonds and couplesmostly to theC1-px,y orbitals. The restoring forcewhen vibrating in the E g2 mode is connected to the partial charge density (∣ ( )∣y r 2) of theC1-px,y states. As showninfigure 4(b), the partial charge density of C1-px,y states around the Fermi level is low and therefore the restoringforce of the E g2 vibration is expected to be small. This in turn puts the E g2 mode of BSiC2 in the low energyregion. The softening of the E g2 mode is an essential account for the highTc in BSiC2. The PL, nonetheless, playsan equally important role. Deduced from equation (9), the required PL for nontrivial contributions tosuperconductivity is of the order of 10–102 GHz, depending on the phonon energies. As shown in table 1, the PLof the E g2 mode inMgB2 is of the order of 103 GHzwhile the corresponding high phonon energy pulls down thestrength of the EPC to lie in themoderate-to-strong regime. In BC3, the high energy of the E g2 mode results in aweaker coupling strength. The special characteristic that BSiC2 bears is that it possesses themerits of having alow-energy E g2 modewhile retaining a relatively large PL. Therefore, the EPC in BSiC2 ismuch stronger thanthat inMgB2, despite a smaller PL. This is also the reasonwhy the strong EPCdoes not cause severe bandsplitting in BSiC2.
The two-gap nature, as is observed inMgB2, is an interesting phenomenon in superconductors. InMgB2, thebroken symmetry of the px,y and pz orbitals of boron leads to two kinds of Fermi surfaces that are significantlydifferent in their band components. These two different kinds of Fermi surfaces couple distinctly to phonons,resulting in two superconducting gaps. Similar withMgB2 electronically, the coexistence of Fermi surfaces withpx,y and pz components in BSiC2 seems to imply the possibility of two distinct superconducting gaps and theanisotropic k-dependence in the EPC. If so, the use of Allen–Dynes–McMillan formula in this work thataverages out the k-dependence of the EPCwould incur an underestimated EPC,whichmeans theTc so obtainedwould be lower than its real value. TakingMgB2 as an example, the calculatedTc with the isotropic picture isabout 25 K. The anisotropy of the EPC and anharmonicity of phonons have to be taken into account toreproduce the experimental value of 39 K [23, 53, 54]. Thus, if BSiC2 really shows the two-gap feature and theconclusion drawn fromMgB2 is also applicable to BSiC2, its realTc would be even higher than the calculatedvalue of 73.6 K and possibly comparable to those of the cuprates. Further investigation on this issue is called for.
4. Conclusion
In summary, we predict a newBCS-superconductor, BSiC2, whoseTc at ambient pressuremay be comparablewith those of cuprates when the possible two-gap nature is taken into account. Its isostructuralmaterial, BC3, isalso predicted to have a ~T 40c K. Similarly, the possible two-gap naturemay further increase its realT .c BSiC2 isdistinct fromother BCS-superconductors in that its strong EPC stems from the significantly softened E g2 modeand the inter-site orbitalfluctuations. The comparison of the resulting EPC andTc withMgB2 and the related
Figure 4.Thewave function of the highest occupied state at G in BSiC2. Top: all atoms sit in their equilibriumpositions. The characterof theC2-p orbital is considerably retained, consistent with the aforementioned little hybridization between the Si–C p-orbitals.Bottom: atoms are displaced as shown infigure 3(c). Charge redistribution betweenC1 andC2 is obviously seen. Left and right panelsrepresent the top and side views, respectively. Although only one unit cell is shown in thisfigure, a 1×1×2 supercell is used in thecalculations to account for the out-of-phase vibration of two adjacent unit cells (asq atA point) in zdirection. All plots are displayedwith identical isosurface.
6
New J. Phys. 22 (2020) 033046 P-J Chen andH-T Jeng
systemBC3 supports the peculiar behaviors of the EPC in BSiC2.Wewould like to emphasize that such high-Tc
superconductivity occurs without the need for doping or pressurization.Hydrogen-free crystal structure alsoalleviates the difficulties in sample growth.
Acknowledgments
The authors acknowledgeNational Center forHigh-Performance Computing (NCHC). H-T Jeng also thankssupport fromAS-iMATE-109-13 andCQT-NTHU-MOE, Taiwan. This work is supported by theMinistry ofScience andTechnology, Academia Sinica, National TaiwanUniversity, andNational Tsing-HuaUniversity,Taiwan.
Notes
The authors declare no competing financial interest.
References
[1] Schilling A, CantoniM,Guo JD andOttHR 1993Nature 363 56[2] Kamihara Y,Watanabe T,HiranoMandHosonoH2008 J. Am. Chem. Soc. 130 3296[3] RenZA et al 2008Europhys. Lett. 83 17002[4] RenZA et al 2008Chin. Phys. Lett. 25 2215[5] Tan S et al 2013Nat.Mater. 12 634[6] Ge J F, Liu Z L, LiuC,GaoCL,QianD, XueQK, Liu Y and Jia J F 2015Nat.Mater. 14 285[7] Mazin I I, SinghD J, JohannesMDandDuMH2008Phys. Rev. Lett. 101 057003[8] SomayazuluM,AhartM,Mishra AK,Geballe ZM,BaldiniM,Meng Y, StruzhkinVV andHemley R J 2019 Phys. Rev. Lett. 122 027001[9] Nagamatsu J,NakagawaN,Muranaka T, Zenitani Y andAkimitsu J S 2001Nature 410 63[10] WangY, Plackowski T and JunodA 2001PhysicaC 355 179[11] Bouquet F, Fisher RA, PhillipsNE,HinksDGand Jorgensen JD 2001Phys. Rev. Lett. 87 047001[12] Szabó P, Samuely P, Kačmarčík J, Klein T,Marcus J, Fruchart D,Miraglia S,Marcenat C and JansenAGM2001Phys. Rev. Lett. 87
137005[13] YangHD, Lin J Y, LiHH,Hsu FH, LiuC J, Li SC, YuRC and JinCQ2001Phys. Rev. Lett. 87 167003[14] Tsuda S, Yokoya T, Kiss T, TakanoY, ToganoK,KitoH, IharaH and Shin S 2001Phys. Rev. Lett. 87 177006[15] Giubileo F, RoditchevD, SacksW, LamyR, ThanhDX,Klein J,Miraglia S, Fruchart D,Marcus J andMonod P 2001 Phys. Rev. Lett. 87
177008[16] Laube F,Goll G,Hagel J, LöhneysenHV, Ernst D andWolf T 2001Europhys. Lett. 56 296[17] Bouquet F,Wang Y, Sheikin I, Plackowski T, JunodA, Lee S andTajima S 2002Phys. Rev. Lett. 89 257001[18] Bouquet F,Wang Y, Fisher RA,HinksDG, Jorgensen JD, JunodA and Phillis N E 2001Europhys. Lett. 56 856[19] An JMandPickettWE 2011Phys. Rev. Lett. 86 4366[20] Kortus J,Mazin I I, BelashchenkoKD, AntropovVP andBoyer L L 2001Phys. Rev. Lett. 86 4656[21] BohnenK-P,Heid R andRenker B 2001Phys. Rev. Lett. 86 5771[22] YildirimT et al 2002Phys. Rev. Lett. 87 037001[23] LiuAY,Mazin I I andKortus J 2001Phys. Rev. Lett. 87 087005[24] ChoiH J, Louie SG andCohenML2009Phys. Rev.B 80 064503[25] Oguchi T 2002 J. Phys. Soc. Japan 71 1495[26] RosnerH, Kitaigorodsky A and PickettWE 2002Phys. Rev. Lett. 88 127001[27] Dewhurst J K, Sharma S, Ambrosch-Draxl C and Johansson B 2003Phys. Rev.B 68 020504[28] Bharathi A, JemimaBalaselvi S, PremilaM, SairamTN, ReddyGLN, Sundar C S andHariharan Y 2002 Solid State Commun. 124 423[29] Souptel D,Hossain Z, BehrG, LöserWandGeibel C 2003 Solid State Commun. 125 17[30] FoggAM,Chalker P R,Claridge J B,DarlingGR andRosseinskyM J 2003Phys. Rev.B 67 245106[31] FoggAM,Claridge J B,DarlingGR andRosseinskyM J 2003Chem. Commun. 1348[32] FoggAM,Meldrum J,DarlingGR,Claridge J B andRosseinskyM J 2006 J. Am.Chem. Soc. 128 10043[33] GaoM, LuZ-Y andXiang T 2015Phys. Rev.B 91 045132[34] Bazhirov T, Sakai Y, Saito S andCohenML2014Phys. Rev.B 89 045136[35] Sofo JO, Chaudhari A S andBarberGD2007Phys. Rev.B 75 153401[36] Savini G, Ferrari AC andGiustino F 2010Phys. Rev. Lett. 105 037002[37] Lu S, LiuH,Naumov I I,Meng S, Li Y, Tse J S, Yang B andHemley R J 2016Phys. Rev.B 93 104509[38] DuanD, Liu Y, Tian F, LiD,HuangX, ZhaoZ, YuH, Liu B, TianWandCui T 2014 Sci. Rep. 4 6968[39] LiuH,Naumov I I, HoffmannR, AshcroftNWandHemleyR J 2017Proc. Natl Acad. Sci. USA 114 6990[40] DrozdovAP, EremetsM I, Troyan I A, Ksenofontov V and Shylin S I 2015Nature 525 73[41] MaY,DuanD, LiD, Liu Y, Tian F, YuH,XuC, Shao Z, Liu B andCui T 2015 arXiv:1511.05291[42] FengX, Zhang J, GaoG, LiuH andWangH2015RSCAdv. 5 59292[43] ZhongX,WangH, Zhang J, LiuH, Zhang S, SongH-F, YangG, Zhang L andMaY 2016Phys. Rev. Lett. 116 057002[44] Ribeiro F J andCohenML2004Phys. Rev.B 69 212507[45] Giannozze P et al 2009 J. Phys.: Condens.Matter 21 395502[46] Baroni S, deGironcoli S andDal CorsoA 2001Rev.Mod. Phys. 73 515[47] Allen PB andDynes RC1975Phys. Rev.B 12 905[48] Denteneer P JH and vanHaeringenW1988 Solid State Commun. 65 115[49] OganovAR andGlass CW2006 J. Chem. Phys. 124 244704
7
New J. Phys. 22 (2020) 033046 P-J Chen andH-T Jeng
[50] OganovAR, Lyakhov AOandValleM2011Acc. Chem. Res. 44 227[51] LyakhovAO,Oganov AR, StokesHT andZhuZ 2013Comput. Phys. Commun. 184 1172[52] KongY,DolgovOV, JepsenO andAndersenOK2001Phys. Rev.B 64 020501(R)[53] ChoiH J, RoundyD, SunH,CohenML and Louie SG 2002Nature 418 758[54] ChoiH J, CohenML and Louie SG2003PhysicaC 385 66
8
New J. Phys. 22 (2020) 033046 P-J Chen andH-T Jeng