KITPC 6/1/091 “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) and B. Andrei Bernevig (Princeton University) Paper ref: arXiv: , ,

KITPC 6/1/092 Outline  Introduction  Direct phase-sensitive probe: Novel π-junction  Indirect probes: S/N/S ± Josephson junction Impurity-induced bound states Quasiparticle interference patterns

KITPC 6/1/093 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-T c 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)…

KITPC 6/1/094 Pairing symmetry in two band-{t}-J 1 -J 2 model J1J1 s-wave pairing cosk x +cosk y d-wave pairing cosk x -cosk y J2J2 s-wave pairing cosk x cosk y d wave pairing sink x sink y K. Seo, B. A. Bernevig, and J.P. Hu PRL 101, (2008) Symmetry factors Function peaks at Fermi surfaces

KITPC 6/1/095 Properties of s-wave cosk x cosk y 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

KITPC 6/1/096 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: J. 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: …

KITPC 6/1/097 Novel π-Junction (I): why usual corner-junctions cannot work for s ± ? D. J. Van Harlingen, RMP 67 (1995) Φ/Φ0Φ/Φ0 I c /I 0 Φ/Φ0Φ/Φ0 Y.-R. Zhou et al., arXiv: for Co-doped 122 material. s ± : non-trivial phase structure of SC order parameter in k-space!

KITPC 6/1/098 Novel π-Junction (II) – our proposal * Suggested s-SC with (1) large FS: MgB 2 (a~0.3nm), Be thin film (a~0.23nm); (2) small FS: 2H-NbSe 2 (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 -p - p €€€€ 2 0 p €€ 2 p -p - p €€ 2 0 p €€ 2 p kxkx kyky top s-SC θtθt Iron pnictide, s ± θmθm bottom s-SC θbθb Φ/πΦ/π Φ= θ t -θ b

KITPC 6/1/099 S-N-S ± Junction (I) – basic idea ∆L∆L (x<0) ∆R∆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: 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 = ∆ ε bs = ± ∆ ∆ L = -∆ R = ∆ ε bs = 0 ∆ s > 0 s-SC ∆ 1 > 0, ∆ 2 < 0 Iron pnictide

KITPC 6/1/0910 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 |t 1 |) (at x=0within ‘N’ region) (~ ∆ FeAs )

KITPC 6/1/0911 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., ; D. Zhang, ] 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 +

KITPC 6/1/0912 LDOS near the non-magnetic impurity site BdG calculations with V I =4|t 1 | and n e ~2.1 per site on a 32x32 lattice

KITPC 6/1/0913 Bound state energy vs. impurity scattering strength (non-magnetic, intra-orbital) s ± -SC, ∆ coh =0.4|t 1 | [For many impurities, see for instance, Y. Bang et al., PRB 79 (2009)]

KITPC 6/1/0914 LDOS near the magnetic impurity site impurity site: (16,16) The peaks decay quickly after ~3 lattice constants J I s z /2=2

KITPC 6/1/0915 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, ]

KITPC 6/1/0916 Quasi-particle interference (QPI): some parameters DOS for a clean s ± -SC Pairing symmetry: ∆ 0 cosk x cosk y (∆ 0 / W ~ 0.01) V imp = 4 ∆ 0 such that N 0 V imp < 1, i.e., in the weak scattering (perturbative) regime ∆ coh ~ 0.08 (in units of |t 1 |)

KITPC 6/1/0917 non- magnetic QPI: induced LDOS(q,ω) for cosk x cosk y s-SC magnetic ω=-0.09 large peaks around (0,0) qxqx qyqy qyqy qxqx peaks around (±π,0)/ (0,±π)

KITPC 6/1/0918 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: F Wang et al., EPL 85, (2009) QPI: induced DOS(q,ω) for |cosk x cosk y | s-SC non-magneticmagnetic

KITPC 6/1/0919 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 cosk x cosk y s-wave pairing symmetry, which changes sign between electron and hole Fermi pockets, we have shown:

KITPC 6/1/0920 Thank you very much for your attention!

KITPC 6/1/0921 Supplement

KITPC 6/1/0922 sign-changed s-wave Nature 453 (2008) arXiv: PRL 102 (2009)

KITPC 6/1/0923 Large FS Small FS

KITPC 6/1/0924 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

KITPC 6/1/0925 QP spectrum in SNS ± junction

KITPC 6/1/0926 Model Hamiltonian in Iron Pnictides

KITPC 6/1/0927 T-matrix for impurity-induced bound states

KITPC 6/1/0928 Non-magnetic S x2y2 S magnetic X

KITPC 6/1/0929 SC gap: non-magnetic impurity S x2y2 S

KITPC 6/1/0930 SC gap: magnetic impurity S x2y2 S

KITPC 6/1/0931 Spatial distribution of Spin-resolved LDOS at positive bound state energy

KITPC 6/1/0932 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

KITPC 6/1/0933 QPI along special directions Intra-orbital scattering dominates

KITPC 6/1/0934 Two-Orbital: d wave NON-magnetic magnetic ω= 0ω= 0.03ω= 0.07 within the gap

KITPC 6/1/0935 Five-Orbital: QPI NON-magnetic magnetic

KITPC 6/1/0936 Five-Orbital: Profiles NON-magnetic magnetic

KITPC 6/1/0937 Five-Orbital: without sign change NON-magneticmagnetic