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

1. “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:0812.0661, 0903.1694, 0905.0734

2. Outline • Introduction • Direct phase-sensitive probe: • Novel π-junction • Indirect probes: • S/N/S± Josephson junction • Impurity-induced bound states • Quasiparticle interference patterns

3. It is critical to determine pairing symmetry in superconducting Iron Pnictides • Many aspects analogous to high-Tc cuprates: • Parent compound is antiferromagnetic albeit metallic • (possibly proximate to a Mott insulator) • (2) Quasi-2D nature (superconductivity related to the FeAs layer) New features: multi-orbital nature and complex Fermi surfaces J. Zhao et al., Nature Materials 7 (2008) Many theoretical proposals for pairing symmetry: For instance, triplet s-wave, nodal s-wave, d-wave, p-wave, extended s-wave (s±)…etc. 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)…

4. Pairing symmetry in two band-{t}-J1-J2 model s-wave pairing coskx+cosky + + + + J1 - + d-wave pairing coskx-cosky + - s-wave pairing coskxcosky J2 d wave pairing sinkxsinky + + + + + - Function peaks at Fermi surfaces Symmetry factors + - K. Seo, B. A. Bernevig, and J.P. Hu PRL 101, 206404 (2008)

5. 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

6. 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: 0812.4416 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: 0901.1895 …

7. Ic/I0 Φ/Φ0 Ic/I0 Φ/Φ0 Novel π-Junction (I): why usual corner-junctions cannot work for s±? Y.-R. Zhou et al., arXiv:0812.3295 for Co-doped 122 material. s±: non-trivial phase structure of SC order parameter in k-space! D. J. Van Harlingen, RMP 67 (1995)

8. + - + top s-SC θt p Iron pnictide, s± θm - + ky θb p €€ € € 2 - bottom s-SC 0 Φ= θt -θb - + + p - €€ € € 2 kx - p p p 0 - p p - €€ € € €€ € € 2 2 Φ/π Novel π-Junction (II) – our proposal Key assumption: momentum conserved after tunneling between layers – high-quality interfaces may be required *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.

9. ∆L ∆R (x<0) (x>0) Within WKJB approximation, the junction can be described by a continuum BdG eq. where Andreev bound state solutions ~ e -γ|x| ∆L = ∆R = ∆ ∆L = -∆R = ∆ εbs = ± ∆ εbs = 0 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) S-N-S± Junction (I) – basic idea ∆s > 0 s-SC ∆1 > 0, ∆2 < 0 Iron pnictide [ ∆λ(x), s-SC order parameter; λcould be a band index ]

10. (at x=0within ‘N’ region) (~ ∆FeAs) (in units of |t1|) 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

11. Self-consistent BdG (on 32x32 lattice) T-matrix Approximation + Detection of the (phase) sign change through impurity effects • Questions for s±-SC: • 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) Strategy: “Hamiltonian” =2-orbital model + a localized single impurity (non-magnetic/magnetic, intra-orbital/inter-orbital)

12. LDOS near the non-magnetic impurity site BdG calculations with VI=4|t1| and ne~2.1 per site on a 32x32 lattice

13. 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)]

14. impurity site: (16,16) LDOS near the magnetic impurity site JIsz/2=2 The peaks decay quickly after ~3 lattice constants

15. 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]

16. Quasi-particle interference (QPI): some parameters Pairing symmetry: ∆0 coskx cosky (∆0 / W ~ 0.01) DOS for a clean s±-SC ∆coh ~ 0.08 (in units of |t1|) Vimp = 4 ∆0 such that N0Vimp < 1, i.e., in the weak scattering (perturbative) regime

17. ω=-0.09 ω=-0.09 QPI: induced LDOS(q,ω) for coskx cosky s-SC qy qy non-magnetic magnetic qx qx peaks around(±π,0)/ (0,±π) large peaks around(0,0)

18. QPI: induced DOS(q,ω) for |coskx cosky| s-SC non-magnetic magnetic • 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)

19. Summary Due to the special feature of coskx cosky s-wave pairing symmetry, which changes sign between electron and hole Fermi pockets, we have shown: • A novel tri-layer π-junction. • 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.

20. Thank you very much for your attention!

21. Supplement

22. sign-changed s-wave s-wave PRL 102 (2009) s-wave arXiv:0812.3295 s-wave Nature 453 (2008)

23. Small FS Large FS

24. 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

25. QP spectrum in SNS± junction

26. Model Hamiltonian in Iron Pnictides

27. T-matrix for impurity-induced bound states

28. Non-magnetic magnetic Sx2y2 X S

29. SC gap: non-magnetic impurity Sx2y2 S

30. SC gap: magnetic impurity Sx2y2 S

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

32. 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

33. Intra-orbital scattering dominates QPI along special directions

34. Two-Orbital: d wave NON-magnetic magnetic ω= 0 ω= 0.03 ω= 0.07 within the gap

35. Five-Orbital: QPI NON-magnetic magnetic

36. Five-Orbital: Profiles NON-magnetic magnetic

37. Five-Orbital: without sign change NON-magnetic magnetic