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