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, 3296-3297

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 gapsemiconductor Semi-metal

hole pocket

electron pocket

Johnston, D. C. (2010). Advances in Physics, 59(6), 803–1061.

Folded & Unfolded BZ

FeAs layer unfolded 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. 74 124508

Fermi Surface (unfolded zone)Bands crossing Fermi-level are derived from Fe d-orbitals

Two hole FS at G

Two electron FS at X

Four quasi-2D electron and hole cylinders:

Kemper, A. F., et al. (2010).. New Journal of Physics, 12(7), 073030.

Fermi Surface (folded zone)

Bands crossing Fermi-level are derived from Fe d-orbitals

G (k=(0,0)) M (k=(p,p))

Two hole FS at G

Two electron FS at M

Four quasi-2D electron and hole cylinders:

Mazin, I. I. & Schmalian, J. Physica C 469, 614623 (2009)

SuperconductivityPairing is singlet – NMR (Knight shift) measurementsGrafe, et al., Phys. Rev. Lett. 101, 047003 (2008).

Kuriki et al. Phys. Rev. B 79, 224511 (2009)

Pairing through phonons unlikely because of weak electron-phonon interactionL. Boeri et al. Phys. Rev. Lett. 101, 026403 (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: cvl31κ

k = kelectrons + kphonons

phsph lvT 0

331 βκ Phonons:

Separate contributions using temperature dependence in low temperature limit

Thermal conductivity: Nodal or fully-gapped?

g impurity bandwidth

normal

superconducting

0 1 2 3

3

2

1(0)

)ε(NN

e/D

activated behaviour at low T 0 as T 0 KT

0ke

Fe lTv 031 γκ

finite nodesT

0k

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, 237005 (2008)

Example 2: YBa2Cu3O7

Hill et al.. Phys. Rev. Lett. 92 027001 (2004)

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

Carrington et al., Physica C 469 (2009) 459–468

P

LaFePO: Thermal conductivity

LaFePO: Thermal conductivityPhonons

= 1.2 T3 mW/Kcm (fitted)

= 1.0 T3 mW/Kcm (spec. heat)

Electrons

LaFePO: d-wave?

Universal linear term estimate:3.5 + 8.7 T 2

(up to 400mK)

Quasiclassical d-wave theoryGraf, Yip, Sauls and Rainer, PRB, 53, 15147 (1996)

= 2.9 mW/K2cm

Use spec. heat: C/T = 10.6 mJ/K molKohama et al. JPSJ 77 094715 (2008)

LaFePO: d-wave?

Graf, Yip, Sauls and RainerPRB, 53, 15147 (1996)

Not T3, more T2 – inconsistent with d-wave

LaFePO: Nodal s+/- wave?

Mishra, et al., Phys. Rev. B 80, 224525 (2009)

Non-universal linear term

Qualitatively similar T dependence

LaFePO: Field Dependence

Mishra, et al., Phys. Rev. B 80, 224525 (2009)

Numerical work for nodal s+/-

LaFePO: Wiedemann-Franz Law

Normal state

Scattering Rate

- if d-wave, would expectsignificant Tc suppression

LaFePO: other experimentsPenetration depth

Power law T dependence

Consistent with nodes

Fletcher et al., PRL 102, 147001 (2009)

Thermal conductivity in other iron-based superconductors

Paglione and Greene, Nat. Phys. 6, 645 (2010)

d-wave in KFe2As2?

Scattering rate betweenthese sample differs by factor ~ 10

r0 ~ 0.21 mW cm

r0 ~ 2.2 mW cm

Universal Conductivity!

J. K. Dong et al., Phys. Rev. Lett. 104, 087005 (2010)

J-Ph. Reid et al., (2012) arXiv:1201.3376v1

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 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 withinthe same s+/- symmetry order parameter.

For sufficiently high doping, FS may be altered enough to drive symmetry change froms+/- to d-wave (see Louis Taillefer’s talk in main meeting).

Overdoped theory