Superconducting Gap Symmetry in Iron-based Superconductors: A Thermal Conductivity Perspective

1. Superconducting Gap Symmetry in Iron-based Superconductors: A Thermal Conductivity Perspective Robert W. Hill

2. Acknowledgements • Michael Sutherland (Cambridge) • James Analytis (Stanford) • Ian Fisher (Stanford) • John Dunn (Waterloo, Oxford) • IssamAlkhesho (Waterloo) • William Toews (Waterloo)

3. Iron-based Superconductors • February 2008: Hosono and co-workers, superconductivity in LaFeAs(O,F), Tc~26 K J. AM. CHEM. SOC. 2008, 130, 3296-3297

4. Iron-based Superconductors Paglione and Greene, Nat. Phys. 6, 645 (2010) 122 family 1111 family Mazin, Nature, 464, 183 (2010)

5. contrast 1: cuprate phase diagram Laboratoire National des Champs MagnétiquesIntenses - Toulouse

6. Semi-metallic character hole pocket electron pocket Indirect band gap semiconductor Semi-metal Johnston, D. C. (2010). Advances in Physics, 59(6), 803–1061.

7. Folded & Unfolded BZ folded BZ (blue) (2-Fe sites) FeAs layer unfolded BZ (green) (1-Fe site) Hirschfeld, P. J., Korshunov, M. M., & Mazin, I. I. (2011). Reports on Progress of physics. 74 124508

8. Fermi Surface (unfolded zone) Bands crossing Fermi-level are derived from Fe d-orbitals Four quasi-2D electron and hole cylinders: Two hole FS at G Two electron FS at X Kemper, A. F., et al. (2010).. New Journal of Physics, 12(7), 073030.

9. Fermi Surface (folded zone) G(k=(0,0)) M(k=(p,p)) Bands crossing Fermi-level are derived from Fe d-orbitals Four quasi-2D electron and hole cylinders: Two hole FS at G Two electron FS at M Mazin, I. I. & Schmalian, J.PhysicaC 469, 614623 (2009)

10. Superconductivity Pairing is singlet – NMR (Knight shift) measurements Grafe,et al., Phys. Rev. Lett. 101, 047003 (2008). Pairing through phonons unlikely because of weak electron-phonon interaction L. Boeri et al. Phys. Rev. Lett. 101, 026403 (2008) Separate concepts of gap symmetry from gap structure Kurikiet al. Phys. Rev. B 79, 224511 (2009)

11. contrast 2: cuprate gap symmetry d wave s wave Scalapino, D. J. (1995). Physics Reports, 250(6), 329–365

12. Thermal conductivity in superconducting state k = kelectrons + kphonons Separate contributions using temperature dependence in low temperature limit Kinetictheory formulation: Phonons:

13. 3 2 superconducting normal 1 0 1 2 3 e/D finite nodes Thermal conductivity: Nodal or fully-gapped? Fully gapped (s-wave) Nodal (d-wave) g impurity bandwidth activatedbehaviour at low T 0 as T 0 K

14. Example 1: filled-skutterudite materials Finite value establishes presence of nodes Consistent with fully gapped superconducting state Hill et al., Phys. Rev. Lett. 101, 237005 (2008)

15. Example 2: YBa2Cu3O7 Hill et al.. Phys. Rev. Lett. 92 027001 (2004)

16. LaFePO (1111 family) • Stoichiometric superconductor, Tc = 7 K, non-magnetic groundstate • Isostructural to LaFeAsO, non-superconducting (dope with F to get Tc~26 K) • FS established from dHvA and ARPES • Anisotropy in transport measurements ~ 15-20 • Single crystal sample • RRR 85 • Small sample (100 x 75 x 25) mm3 • Contacts made using evaporated gold pads P Carrington et al., PhysicaC 469 (2009) 459–468

17. LaFePO: Thermal conductivity

18. LaFePO: Thermal conductivity Phonons = 1.2 T3mW/Kcm (fitted) = 1.0 T3mW/Kcm (spec. heat) Electrons

19. LaFePO: d-wave? Quasiclassicald-wave theory Graf, Yip, Sauls and Rainer, PRB, 53, 15147 (1996) 3.5 + 8.7 T 2 (up to 400mK) Universal linear term estimate: = 2.9 mW/K2cm Use spec. heat: C/T = 10.6 mJ/K mol Kohama et al. JPSJ 77 094715 (2008)

20. LaFePO: d-wave? Graf, Yip, Sauls and Rainer PRB, 53, 15147 (1996) Not T3, more T2 – inconsistent with d-wave

21. LaFePO: Nodal s+/- wave? Non-universal linear term Qualitatively similar T dependence Mishra, et al., Phys. Rev. B 80, 224525 (2009)

22. LaFePO: Field Dependence Numerical work for nodal s+/- Mishra, et al., Phys. Rev. B 80, 224525 (2009)

23. LaFePO: Wiedemann-Franz Law Scattering Rate Normal state • if d-wave, would expect • significant Tc suppression

24. LaFePO: other experiments Penetration depth Power law T dependence Consistent with nodes Fletcher et al., PRL 102, 147001 (2009)

25. Thermal conductivity in other iron-based superconductors Paglione and Greene, Nat. Phys. 6, 645 (2010)

26. d-wave in KFe2As2? Scattering rate between these sample differs by factor ~ 10 r0 ~ 0.21 mW cm r0 ~ 2.2 mW cm Universal Conductivity! J-Ph. Reid et al., (2012) arXiv:1201.3376v1 J. K. Dong et al., Phys. Rev. Lett. 104, 087005 (2010)

27. Summary and Conclusions LaFePO Finite residual electronic conduction in zero temperature limit - evidence for nodes in superconducting gap. Quantitatively consistent with universal d-wave value -However, electronic temperature dependence qualitatively inconsistent (not T3). Qualitatively consistent with nodal s+/- wave. -Require methodical impurity dependence and numerical quantitative analysis. In broader picture of iron-based superconducting families, the sensitivity of the gap topology to Fermi surface details (because of a magnetic coupling mechanism) makes the observation of both nodes and fully-gapped structure a possibility within the same s+/- symmetry order parameter. For sufficiently high doping, FS may be altered enough to drive symmetry change from s+/- to d-wave (see Louis Taillefer’s talk in main meeting).

28. Overdoped theory