Low Temperature Thermal Transport Across the Cuprate Phase Diagram
Mike Sutherland
Louis Taillefer Rob Hill Cyril Proust Filip Ronning Makariy Tanatar
Christian Lupien Etienne Boaknin Dave Hawthorn J. Paglione M. Chiao
R.Gagnon, H.Zhang D.Bonn, R.Liang, W.Hardy P.Fournier, R.Greene A.P.Mackenzie, D. Peets, S. Wakimoto
Department of Physics University of Toronto
What questions can we address by studying low temperature thermal conductivity as a function of doping in the cuprates ? How well does d-wave BCS theory describe the superconducting state ?
m a g n e t i s m
pseudogap
Is the superconducting order parameter pure d-wave throughout the phase diagram?
metal
Temperature
superconductor
Carrier concentration
How does the pseudogap influence the behaviour of low-energy quasiparticles?
The density of states in a d-wave superconductor density of states
presence of nodes quasiparticles at low T
g
clean limit
Linear density of states at low energy - governs all low temperature properties
impurity bandwidth
impurity effects
Finite density of delocalised states at zero energy
Fermi Liquid Theory of d-wave Nodal Quasiparticles
d-wave gap: = 0cos(2)
E
The quasiparticle excitation spectrum near the nodes takes the form of a ‘Dirac cone’ :
E v F k1 v 2 k 2
2 2 2
2
With:
v2
1 k F node
Thermal Conductivity Primer
l A
κe
e 1 3 γTvF l0
3 ph 1 3 βT vs l0
T
Q
Q l κ T A
κ T
κ ph
k = kelectrons + kphonons
Kinetic theory formulation:
phonons ~ T3
κ cvl
1 3
0
electrons ~ T
T2
d-wave BCS theory of thermal conductivity
Cooper pairs carry no heat Electronic heat transport provided solely by quasiparticles (T 0, T<