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

Acknowledgements Michael Sutherland (Cambridge) James Analytis (Stanford) Ian Fisher (Stanford) John Dunn (Waterloo, Oxford) Issam Alkhesho (Waterloo) William Toews (Waterloo)

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

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

contrast 1: cuprate phase diagram Laboratoire National des Champs Magnétiques Intenses - Toulouse

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

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

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

Fermi Surface (folded zone) Bands crossing Fermi-level are derived from Fe d-orbitals  (k=(0,0))  (k=(  )) Two hole FS at  Two electron FS at M Four quasi-2D electron and hole cylinders: Mazin, I. I. & Schmalian, J. Physica C 469, (2009)

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

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

Thermal conductivity in superconducting state Kinetic theory formulation:  =  electrons +  phonons Phonons: Separate contributions using temperature dependence in low temperature limit

Thermal conductivity: Nodal or fully-gapped?  impurity bandwidth normal superconducting  activated behaviour at low T 0 as T 0 K finite nodes Fully gapped (s-wave)Nodal (d-wave)

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

Example 2: YBa 2 Cu 3 O 7 Hill et al.. Phys. Rev. Lett (2004)

LaFePO (1111 family) Stoichiometric superconductor, T c = 7 K, non-magnetic groundstate Isostructural to LaFeAsO, non-superconducting (dope with F to get T c ~26 K) FS established from dHvA and ARPES Anisotropy in transport measurements ~ Single crystal sample RRR 85 Small sample (100 x 75 x 25)  m 3 Contacts made using evaporated gold pads Carrington et al., Physica C 469 (2009) 459–468 P

LaFePO: Thermal conductivity

Phonons = 1.2 T 3 mW/Kcm (fitted) = 1.0 T 3 mW/Kcm (spec. heat) Electrons

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

LaFePO: d-wave? Graf, Yip, Sauls and Rainer PRB, 53, (1996) Not T 3, more T 2 – inconsistent with d-wave

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

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

LaFePO: Wiedemann-Franz Law Normal state Scattering Rate - if d-wave, would expect significant T c suppression

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

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

d -wave in KFe 2 As 2 ? Scattering rate between these sample differs by factor ~ 10  0 ~ 0.21  cm  0 ~ 2.2  cm Universal Conductivity! J. K. Dong et al., Phys. Rev. Lett. 104, (2010) J-Ph. Reid et al., (2012) arXiv: v1

Summary and Conclusions Finite residual electronic conduction in zero temperature limit - evidence for nodes in superconducting gap. LaFePO Quantitatively consistent with universal d-wave value - However, electronic temperature dependence qualitatively inconsistent (not T 3 ). 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).

Overdoped theory