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
Paglione and Greene, Nat. Phys. 6, 645 (2010)
122 family
1111 family
Mazin, Nature, 464, 183 (2010)
contrast 1: cuprate phase diagram
Laboratoire National des Champs Magnétiques Intenses - Toulouse
Semi-metallic character
hole pocket
electron pocket
Indirect band gap
semiconductor
Semi-metal
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
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.
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. Physica C 469, 614623 (2009)
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
Kuriki et al. Phys. Rev. B 79, 224511 (2009)
contrast 2: cuprate gap symmetry
s wave
d wave
Scalapino, D. J. (1995). Physics Reports, 250(6), 329–365
Thermal conductivity in superconducting state
k = kelectrons + kphonons
Separate contributions using temperature dependence in low temperature limit
Kinetic theory formulation:
Phonons:
κ  13 cvl
κ ph  13 βT 3vsl0ph
Thermal conductivity: Nodal or fully-gapped?
Fully gapped (s-wave)
Nodal (d-wave)
3
N (ε )
N (0)
2
superconducting
normal
1
0
1
2
e/D
3
activated behaviour at low T
k0
0 as T 0 K
T
g
impurity bandwidth
κ e  13 γTvF l0e
finite
k0
T
nodes
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
P
Carrington et al., Physica C 469 (2009) 459–468
LaFePO: Thermal conductivity
LaFePO: Thermal conductivity
Phonons
= 1.2 T3 mW/Kcm (fitted)
= 1.0 T3 mW/Kcm (spec. heat)
Electrons
LaFePO: d-wave?
Quasiclassical d-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)
LaFePO: d-wave?
Graf, Yip, Sauls and Rainer
PRB, 53, 15147 (1996)
Not T3, more T2 – inconsistent with d-wave
LaFePO: Nodal s+/- wave?
Non-universal linear term
Qualitatively similar T dependence
Mishra, et al., Phys. Rev. B 80, 224525 (2009)
LaFePO: Field Dependence
Numerical work for nodal s+/-
Mishra, et al., Phys. Rev. B 80, 224525 (2009)
LaFePO: Wiedemann-Franz Law
Scattering Rate
Normal state
- if d-wave, would expect
significant Tc suppression
LaFePO: other experiments
Penetration 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 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)
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).
Overdoped theory