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“Possible probes for detecting s±-wave pairing symmetry in Iron-Pnictides:

Novel Josephson junctions and impurity effects”

Wei-Feng Tsai

Xiao-Ting Zhou, Chen Fang, Kangjun Seo, Yan-Yang Zhang, Dao-Xin Yao, JiangPing Hu

(Purdue University)

andB. Andrei Bernevig(Princeton University)

Paper ref: arXiv:0812.0661, 0903.1694, 0905.0734

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Outline

IntroductionDirect phase-sensitive probe:

• Novel π-junction

Indirect probes:• S/N/S± Josephson junction

• Impurity-induced bound states• Quasiparticle interference patterns

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It is critical to determine pairing symmetry in superconducting Iron Pnictides

New features: multi-orbital nature and complex Fermi surfaces

Many theoretical proposals for pairing symmetry: For instance, triplet s-wave, nodal s-wave, d-wave, p-wave, extended s-wave (s±)…etc.

Many aspects analogous to high-Tc cuprates:

(1) Parent compound is antiferromagnetic albeit metallic

(possibly proximate to a Mott insulator)(2) Quasi-2D nature (superconductivity related

to the FeAs layer)

J. Zhao et al., Nature Materials 7 (2008)

X. Dai et al., PRL 101 (2008); K. Kuroki et al., PRL 101 (2008); M. Daghofer et al., PRL 101 (2008); Q. Si and E. Abarahams, PRL 101 (2008); P.A. Lee and X.G. Wen, PRB 78 (2008); I. Mazin et al., PRL (2008)…

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Pairing symmetry in two band-{t}-J1-J2 model

J1

s-wave pairingcoskx+cosky

d-wave pairingcoskx-cosky

J2

s-wave pairingcoskxcosky

d wave pairingsinkxsinky

+-

+

-

K. Seo, B. A. Bernevig, and J.P. Hu PRL 101, 206404 (2008)

++

+

+

+

+

+

+

-

+

+

-

Symmetry factors Function peaks at Fermi surfaces

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Properties of s-wave coskxcosky Pairing Symmetry

Order parameters have different signs at electron and hole pockets

If magnetic exchanges are symmetric for all orbits, gaps should be determined by single energy scale

Superconducting gaps are larger in smaller pockets.

Fermi surfaces are generally gapped unless heavy doping crosses gapless line. Gapless lines

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Alas, most experiments are only sensitive to SC gap magnitudes

Question: How to detect sign-changed s-wave pairing symmetry?

D. Parker and I. Mazin, arXiv: 0812.4416J. Wu and P. Phillips, PRB 79 (2009)X.-Y. Feng and T.-K. Ng, PRB 79 (2009)P. Ghaemi et al., PRL 102 (2009)S. Onari and Y. Tanaka, PRB 79 (2009)J. Linder et al., arXiv: 0901.1895…

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Novel π-Junction (I): why usual corner-junctions cannot work for s±?

D. J. Van Harlingen, RMP 67 (1995)

Φ/Φ0

Ic/I0

Φ/Φ0

Ic/I0

Y.-R. Zhou et al.,arXiv:0812.3295for Co-doped 122material.

s±: non-trivial phase structureof SC order parameter in k-space!

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Novel π-Junction (II) – our proposal

*Suggested s-SC with (1) large FS: MgB2 (a~0.3nm), Be thin film (a~0.23nm); (2) small FS: 2H-NbSe2 (a~0.345nm). Or possibly metallic thin film with large or small FS due to SC proximity effect.

Key assumption: momentum conserved after tunneling between layers – high-quality interfaces may be required

€€€€20 €€€€2

€€€€2

0

€€€€2

kx

ky+ -

-

-

-

++

++

top s-SC θt

Iron pnictide, s± θm

bottom s-SC θb

Φ/π

Φ= θt -θb

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S-N-S± Junction (I) – basic idea

∆L

(x<0)

∆R

(x>0)

[ ∆λ(x), s-SC order parameter;λcould be a band index ]

Within WKJB approximation, the junction can be described by a continuum BdG eq.

where

T.K.Ng and N.Nagaosa, arXiv:0809.3343

For the junction with unconventional pairing symmetries, see e.g. S. Kashiwaya and Y. Tanaka, Rep. Prog. Phys. 72 (2000)

Andreev bound state solutions ~ e -γ|x|

∆L = ∆R = ∆

εbs = ± ∆

∆L = -∆R = ∆

εbs = 0

∆s > 0s-SC

∆1 > 0, ∆2 < 0Iron pnictide

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S-N-S± Junction (II) – QP-LDOS for various pairing symmetries

*A two-orbital exchange coupling model on the lattice is used for Iron pnictides

(in units of |t1|)

(at x

=0w

ithi

n ‘N

’ re

gion

)

(~ ∆FeAs)

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Detection of the (phase) sign change through impurity effects

Strategy:

“Hamiltonian” =2-orbital model + a localized single impurity (non-magnetic/magnetic, intra-orbital/inter-orbital)

Questions for s±-SC:

1) Any non-trivial in-gap bound-states? (E < ∆coh) [See also T. Zhou et al., 0904.4273; D.

Zhang, 0904.3708]

2) What does the quasi-particle interference pattern look like? [Also suggested by Fa Wang et al. in EPL 85 (2009)]

A. V. Balatsky et al, RMP (2006)J. E. Hoffman et al, Science 297 (2002)

Q.H. Wang and D.H. Lee, PRB (2003)

Self-consistent BdG (on 32x32 lattice)

T-matrix Approximation

+

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LDOS near the non-magnetic impurity site

BdG calculations with VI=4|t1| and ne~2.1 per site on a 32x32 lattice

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Bound state energy vs. impurity scattering strength (non-magnetic, intra-orbital)

s±-SC, ∆coh=0.4|t1|

[For many impurities, see for instance, Y. Bang et al., PRB 79 (2009)]

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LDOS near the magnetic impurity site

impurity site: (16,16)

The peaks decay quickly after ~3 lattice constants

JIsz/2=2

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Quantum phase transition (level-crossing) and subtle features

(1) In-gap bound states are more robust (2) No πphase shift at the impurity site

[For strong “inter-band” magnetic scattering, see Jian Li and Y. Wang, 0905.3883]

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Quasi-particle interference (QPI): some parameters

DOS for a clean s±-SC

Pairing symmetry: ∆0 coskx cosky (∆0 / W ~ 0.01)

Vimp = 4 ∆0 such that N0 Vimp < 1, i.e., in the weak scattering (perturbative) regime

∆coh ~ 0.08

(in units of |t1|)

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non-magnetic

QPI: induced LDOS(q,ω) for coskx cosky s-SC

magnetic

ω=-0.09 ω=-0.09

large peaks around (0,0)

qx

qyqy

qx

peaks around (±π,0)/ (0,±π)

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In sign-changed s-wave pairing states: The peaks around (π,0)/(0,π) show up for the case of non-magnetic impurity Anti-correlation between the intensities around (0,0) and (π,0)/(0,π)

Y.Y. Zhang et al., arXiv:0903.1694

F Wang et al., EPL 85, 37005 (2009)

QPI: induced DOS(q,ω) for |coskx cosky| s-SCnon-magnetic magnetic

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Summary

1. A novel tri-layer π-junction.

2. The presence of non-trivial in-gap bound states in the S-N-S± Josephson junction, sharply in contrast to other

singlet pairing states.

3. A non-magnetic impurity in s±-SC can induce in-gap bound states in sharp contrast to conventional s-wave SC.

4. The presence (absence) of (0,π) / (π,0) peaks in QPI for s±-SC with non-magnetic (magnetic) impurities is a distinguishable feature compared with conventional s-SC.

Due to the special feature of coskx cosky s-wave pairing symmetry, which changes sign between electron and hole Fermi pockets, we have shown:

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Thank you very much for your attention!

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Supplement

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sign-changeds-wave

s-wave

s-wave

s-wave

Nature 453 (2008)

arXiv:0812.3295

PRL 102 (2009)

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Large FS Small FS

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With finite width d of the N region, the bound state energy appears at

With unequal magnitudes of pairing potentials,

provided

Formula in SNS junction

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QP spectrum in SNS± junction

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Model Hamiltonian in Iron Pnictides

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T-matrix for impurity-induced bound states

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Non-magnetic

Sx2y2

S

magnetic

X

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SC gap: non-magnetic impurity

Sx2y2

S

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SC gap: magnetic impuritySx2y2

S

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Spatial distribution of Spin-resolved LDOS at positive bound state energy

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T-Matrix approximation for induced LDOS

The single-impurity induced Green’s function is

The standard perturbation theory gives

Therefore the Fourier transform of the induced LDOS is

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QPI along special directions

Intra-orbital scattering dominates

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Two-Orbital: d wave

NON-magnetic

magnetic

ω= 0 ω= 0.03 ω= 0.07

within the gap

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Five-Orbital: QPI

NON-magnetic

magnetic

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Five-Orbital: Profiles

NON-magnetic magnetic

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Five-Orbital: without sign change

NON-magnetic magnetic