low temperature thermal transport across the cuprate phase diagram mike sutherland
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Department of Physics University of Toronto
Low Temperature Thermal Transport Across the Cuprate Phase Diagram
Mike Sutherland
Louis TailleferRob HillCyril ProustFilip RonningMakariy Tanatar
R.Gagnon, H.ZhangD.Bonn, R.Liang, W.HardyP.Fournier, R.GreeneA.P.Mackenzie, D. Peets, S. Wakimoto
Christian LupienEtienne BoakninDave HawthornJ. PaglioneM. Chiao
Carrier concentration
superconductor
metal
magnetism
Tem
pera
ture
pseudogap
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 ?
Is the superconductingorder parameter pure d-wave throughout the phase diagram?
How does the pseudogapinfluence the behaviour oflow-energy quasiparticles?
The density of states in a d-wave superconductor
impurity effects
Finite density of delocalised states at zero energy
density of states
impurity bandwidth
presence of nodes quasiparticles at low T
Linear density of states at low energy- governs all low temperature properties
clean limit
Fermi Liquid Theory of d-wave Nodal Quasiparticles
22
22
21
2F kvkvE
With:
node
2
1v
Fk
The quasiparticle excitation spectrum near the nodes takes the form of a ‘Dirac cone’ :
d-wave gap: = 0cos(2)
E
Thermal Conductivity Primer
lA
Q
Kinetic theory formulation:
cvl31κ
= electrons + phonons
eFe lTv 03
1 γκ
phsph lvT 0
331 βκ A
l
T
Q
κ
T
κ
2T
electrons ~ T
phonons ~ T3
0
d-wave BCS theory of thermal conductivity
F
F
v
v
v
v 2
2
2B0
d
n
3
k
T
κ
Electronic heat transport provided solely by quasiparticles
( T0, T<<)
A. Durst and P. A. Lee, Phys. Rev. B 62, 1270 (2000).M. J. Graf et al., Phys. Rev. B 53,15147 (1996).
This result is universal universal with respect to impurity concentration
Cooper pairs carry no heat
)(21
v 0
node
2 wavedkk FF
Δo from κ0/T
Optimally Doped Bi-2212
192
F
cmK
mW
T 20 15.0
cm/s105.2 7Fv
cm/s1023.1 62 v
2v
vF
Ding et al. PRB 54 (1996) R9678 Mesot et al. PRL 83 (1999) 840
ARPES:
Nodal quasiparticles in optimally doped Cuprates
FF kkwaved
0
node
2
21)(v
Weak Coupling BCS:
0 = 2.14kBTc= 17 meV
0 = 30 meV
Increase Coupling:
0 4kBTc
M.Chiao et al. PRB 62 3554 (2000)
doping dependence: vF
15 ms10x 5.2~ FX.J. Zhou et. al. Nature 423 398 ( 2003 )
LSCO(x)
Fk1
)(v
k
kEF
essentially doping independent
Nodal quasiparticles in overdoped Cuprates
How do we estimate hole concentration [p]?
overdoped Tl 2201
2max
)16.0(6.821 pT
T
c
c
Dopin
g
Tc=15 K sample: Proust et al., PRL 89 147003 (2002).
Tc = 15K
Tc = 27K
Tc = 89K
Tc = 85K
0 = 4kBTc
Other samples: Hawthorn et. al. to be published
underdoped YBCO
Nodal quasiparticles in underdoped Cuprates
vF/v2 as doping
0/T as doping
decr
ease
decr
ease
decr
ease
decr
ease simple BCS theory violated:
Δo does not follow ΔBCS !
Sutherland et al. PRB (2003)
The pseudogap in underdoped Cuprates
pseudogap is : (i) quasiparticle gap (ii) must have nodes
(iii) must have linear dispersion
Campuzano et. al. PRL 83 (1999) 3709Norman et. al. Nature 392, 157 (1998)White et. al. Phys. Rev. B. 54, R15669 (1996)Loeser et. al. Phys. Rev. B. 56, 14185 (1996)
T = 15 K
Underdoped La2-xSrxCuO4
0
100
200
300
400
0.05 0.1 0.15 0.2 0.25
Linear Term vs. Doping
linear term YBCOlinear term LSCO
0 /
T [ W
/K2cm
]
hole concentration [ p ]
0
10
20
30
40
0.02 0.04 0.06 0.08 0.1
LSCO: low dopings
0 /
T [ W
/K2 cm
]
hole concentration [ p ]
2/3(kBh/2n/d)
F
F
v
v
v
v 2
2
2B0
d
n
3
k
T
κ
Presence of static SDW order?
Large intrinsic crystalline disorder?
Summary and Outlook
doping dependence of superconducting gap maximum :
overdoped – optimal doped: 0 scales with Tc (BCS theory)
optimal doped – underdoped: 0 increases while Tc decreases(Failure BCS theory)
Question: What happens near the AF – SC boundary?
existence of nodes throughout the phase diagram:
no evidence for quantum phase transition to d+ix in the bulk
doping dependence: vF
essentially doping independent15 ms10x 5.2~ F
ARPES data Z.X.Shen
LSCO(x)
Fk1
)(v
k
kEF
Specular Reflection of Phonons
Specular reflection lph = f(T)
ph/T~ T, <2
R. O. Pohl* and B. Stritzker, PRB 25, 3608 (1982).
Sapphire
V3Si s-wave SC (thermal insulator, el =0)
Fit data to /T = o/T + BT o/T = 0
= 1.7
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