Transcript Document

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 ?
Temperature
How well does d-wave
BCS theory describe the
superconducting state ?
m
a
g
n
e
t
i
s
m
Is the superconducting
order parameter pure
d-wave throughout
the phase diagram?
pseudogap
metal
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 

kF  node
Thermal Conductivity Primer
l
A
Q
T
κ e  13 γTvF l0e
Q l
κ
T A
k = kelectrons + kphonons
κ ph 
3
ph
1
3 βT vsl0
κ
T
phonons ~ T3
Kinetic theory formulation:
κ  cvl
1
3
electrons ~ T
0
T2
d-wave BCS theory of thermal conductivity
Cooper pairs carry no heat
Δo from κ0/T
Electronic heat transport
provided solely by quasiparticles
(T
0, T<<g )
κ 0 k 2B n  vF v2 
  

T 3 d  v2 vF 
This result is universal with
respect to impurity concentration
A. Durst and P. A. Lee, Phys. Rev. B 62, 1270 (2000).
M. J. Graf et al., Phys. Rev. B 53,15147 (1996).
v2 
2
1 

 0 (d  wave)
k F  node k F
Nodal quasiparticles in optimally doped Cuprates
Optimally Doped Bi-2212
v 2 (d  wave) 
k0
T
 0.15
mW
K 2 cm 
F
 19
2
2
1 

 0
k F  node k F
0 = 30 meV
Weak Coupling BCS:
0 = 2.14kBTc= 17 meV
Increase Coupling:
6
ARPES: v2  1.2310 cm/s
vF  2.5 107 cm/s
M.Chiao et al. PRB 62 3554 (2000)
vF
 
v2
0  4kBTc
Ding et al. PRB 54 (1996) R9678 Mesot et al. PRL 83 (1999) 840
(,p)
(p,p)
doping dependence: vF
G
(p,)

E (k )
vF 
k1 k
LSCO(x)
 F ~ 2.5 x 105 ms1 essentially doping independent
X.J. Zhou et. al. Nature 423 398 ( 2003 )
F
Nodal quasiparticles in overdoped Cuprates
overdoped Tl 2201
Tc = 15K
Doping
Tc = 27K
Tc = 89K
0 = 4kBTc
Tc = 85K
How do we estimate hole concentration [p]?
Tc
2

1

82
.
6
(
p

0
.
16
)
Tcmax
Tc=15 K sample: Proust et al., PRL 89 147003 (2002).
Other samples: Hawthorn et. al. to be published
Nodal quasiparticles in underdoped Cuprates
underdoped YBCO
k0/T
vF/v2
as doping
as doping
simple BCS theory violated:
Δo does not follow ΔBCS !
Sutherland et al. PRB (2003)
The pseudogap in underdoped Cuprates
(,p)
(p,p)
G
(p,)
T = 15 K
Campuzano et. al. PRL 83 (1999) 3709
Norman et. al. Nature 392, 157 (1998)
White et. al. Phys. Rev. B. 54, R15669 (1996)
Loeser et. al. Phys. Rev. B. 56, 14185 (1996)
pseudogap is : (i) quasiparticle gap
(ii) must have nodes
(iii) must have linear dispersion
Underdoped La2-xSrxCuO4
Linear Term vs. Doping
300
κ 0 k 2B n  vF v2 
  

T 3 d  v2 vF 
linear term YBCO
linear term LSCO
200
100
LSCO: low dopings
40
0.1
0.15
0.2
0.25
hole concentration [ p ]
Presence of static SDW order?
Large intrinsic crystalline disorder?
0
0.05
2/3(k h/2p)(n/d)
B
30
2
0
k / T [ W/K cm ]
0
2
k / T [ W/K cm ]
400
20
10
0
0.02
0.04
0.06
0.08
hole concentration [ p ]
0.1
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)
existence of nodes throughout
the phase diagram:
no evidence for quantum phase transition
to d+ix in the bulk
Question: What happens near the AF – SC boundary?
(,p)
(p,p)
doping dependence: vF
G
(p,)

E (k )
vF 
k1 k
LSCO(x)
ARPES data Z.X.Shen
 F ~ 2.5 x 105 ms1 essentially doping independent
F
Specular Reflection of Phonons
V3Si s-wave SC
(thermal insulator, kel =0)
 = 1.7
Sapphire
Specular
reflection lph = f(T)
kph/T~ T,  <2
Fit data to
k/T = ko/T + BT
R. O. Pohl* and B. Stritzker, PRB 25, 3608 (1982).
ko/T = 0