Transcript What lies above: the vortex liquid above Tc in cuprate superconductors. Yayu Wang, LuLi, J.

What lies above: the vortex liquid above Tc in
cuprate superconductors.
Yayu Wang, LuLi, J. Checkelsky, N.P.O. Princeton Univ.
M. J. Naughton, Boston College
1.
2.
3.
4.
5.
Vortex Nernst effect
Loss of long-range phase coherence
The Upper Critical Field
High-temperature Diamagnetism
KT vs 3DXY: phase-correlation length
S. Uchida, Univ. Tokyo
Yoichi Ando, Elec. Power U., Tokyo
Genda Gu, Brookhaven
S. Onose, Y. Tokura, U. Tokyo
B. Keimer, MPI Stuttgart
St. Andrews June 2005
Phase diagram of Cuprates
Mott insulator
s = 1/2
T*
T
pseudogap
Tc
AF
0
dSC
Fermi
liquid
0.25
0.05
doping x
hole
Vortex in cuprates
Vortex in Niobium
b(r)
Normal core
CuO2 layers
superfluid
electrons
Js
Js
H
x
x
2D vortex pancake
Gap D(r) vanishes in core
|Y| = D
The Josephson Effect, phase-slippage and Nernst signal
Passage of a vortex
Phase diff.  jumps by 2
Phase difference
vortex

2
2eVJ =  

2eVJ = 2  nV

VJ
Integrate VJ to give dc signal
prop. to nv
t
Nernst experiment
ey
Hm
Vortices move in a temperature gradient
Phase slip generates Josephson voltage
Nernst signal
ey = Ey /|
2eVJ = 2h nV
EJ = B x v
H
T|
Nernst effect in underdoped LSCO-0.12 with Tc = 29K
vortex Nernst signal onset from T = 120 K, ~ 90K above Tc`1
Nernst effect in underdoped Bi-2212 (Tc = 50 K)
Vortex signal persists to 70 K above Tc !
Vortex signal above Tc0 in under- and over-doped Bi 2212
|Y| eiq(r)
Phase rigidity
Long-range phase coherence requires uniform q
“kilometer of dirty lead wire”
q
q
q
Hr = 1
3
d
 r r S (q )
2
2
q
phase rigidity measured by rs
Phase coherence destroyed by vortex motion
q
q
Emery, Kivelson, (1995): Spontaneous vortex creation at Tc in cuprates
Kosterlitz-Thouless transition
Spontaneous vortices destroy superfluidity in 2D films
Change in free energy DF to create a vortex
DF = DU – TDS = (ec – kBT) log (R/a)2
DF < 0 if T > TKT = ec/kB
rs
0
vortices appear spontaneously
D
TKT
TcMF
3D version of KT transition in cuprates?
•Loss of phase coherence determines Tc
•Condensate amplitude persists T>Tc
overdoped
optimum
underdoped
3.5
OD-Bi2212 ( T c =65K)
3.0
50
OPT-Bi2212 ( T c =90K)
3.0
UD-Bi2212 ( T c =50K)
40K
75
45
70K
3.0
45
2.5
40
2.5
55
e y ( m V/K)
3.5
50
2.5
35
2.0
60
30
90
1.5
25 1.0
65
0.5
70
0.0
5
10
85
1.5
60
1.0
65
55
95
70
0.5
75
0
2.0
2.0
1.5
1.0
80
15
m 0 H (T)
20
25
20
80
85 0.0
90
0
30
100
0.5
105
110
5
10
15
m 0 H (T)
20
25
30
0.0
0
Field scale increases as x decreases
5
10
75
80
90
100
15
20
m 0 H (T)
25
30
PbIn, Tc = 7.2 K (Vidal, PRB ’73)
Bi 2201 (Tc = 28 K, Hc2 ~ 48 T)
2.0
T=8K
T=1.5K
e y (m V/K)
1.5
ey
Hd
1.0
0.5
0.0
0.3
Hc2
Hc2
H/Hc2
1.0
0
10
• Upper critical Field Hc2 given by ey
20
30
m 0 H (T)
0.
• Hole cuprates --- Need intense fields.
40
50
60
Vortex-Nernst signal in Bi 2201
• Hc2 increases as x decreases
(like ARPES gap D0)
• Compare x0 (from Hc2) with
Pippard length
xP = hvF/aD0 (a = 3/2)
STM vortex core
xSTM ~ 22 A
Cooper pairing potential
largest in underdoped
regime
D
D0 (Ding)
LSCO
NbSe2
Hole-doped cuprates
NdCeCuO
Hc2
Hc2
Hc2
vortex
liquid
vortex
liquid
Hm
Hm
Hm
Tc0
Conventional SC
Amplitude vanishes
at Tc0 (BCS)
Tc0
Expanded vortex liquid
Amplitude vanishes at
Tc0
Tc0
Vortex liquid dominant.
Loss of phase coherence
at Tc0 (zero-field melting)
Diamagnetic currents in vortex liquid
H
Supercurrents follow contours of condensate
Js = -(eh/m)
x |Y|2 z
Cantilever torque magnetometry
Torque on magnetic moment:  = m × B
crystal

×
B

Deflection of cantilever:  = k 
m
Micro-fabricated single crystal silicon cantilever
magnetometer (Mike Naughton)
H
•
Micro-fabricated Si single-crystal cantilever
•
Very thin cantilever beam: ~ 5 mm
•
•
Capacitive detection of deflection
Sensitivity: ~ 5 × 10-9 emu at 10 tesla
~200 times more sensitive than commercial SQUID
Tc
Tc
110K
• In underdoped Bi-2212, onset of diamagnetic fluctuations at 110 K
• diamagnetic signal closely tracks the Nernst effect
Magnetization curves in underdoped Bi 2212
Tc
Separatrix Ts
At high T, M scales with Nernst signal eN
M(T,H) matches eN in both H and T above Tc
Magnetization in Abrikosov state
M
Hc1
Hc2
H
M = - [Hc2 – H] / b(2k2 –1)
M~ -lnH
In cuprates, k = 100-150, Hc2 ~ 50-150 T
M < 1000 A/m (10 G)
Area = Condensation energy U
Hc2
Hc2
M
T
Tc-
In conventional type II supercond., Hc2
Tc
0
Hc2
Hc2
M
Tc
In cuprates, Hc2 is unchanged as T
Tc
Resistivity Folly
Bardeen Stephen law (not seen)
1.0
N d CCO ( T c =24.5K)
0.8
LSCO (0.20)
0.8
12K
r
22K
e y( m V/K)
e y (m V/K)
0.6
0.4
r
0.6
0.4
ey
ey
0.2
0.2
Hc2
Hc2
0.0
0
2
4
6
8
m 0 H (T)
10
12
14
0.0
0
5
10
15
20
m 0 H (T)
Resistivity does not distinguish vortex liquid and normal state
25
30
Phase fluctuation in cuprate phase diagram
T*
Temperature T
pseudogap
Tonset
vortex liquid
Tc
0
x (holes)
spin pairing
(NMR relaxation,
Bulk suscept.)
Onset of charge pairing
Vortex-Nernst signal
Enhanced diamagnetism
Kinetic inductance
superfluidity
long-range phase coherence
Meissner eff.
Relevant Theories
Doniach Inui (Phys. Rev. B 90)
Loss of phase coherence and charge fluctuation in underdoped regime
Emery Kivelson (Nature 95)
Loss of coherence at Tc in low (superfluid) density SC’s
K. Levin (Rev. Mod. Phys. ‘05)
M. Renderia et al. (Phys. Rev. Lett. ’02)
Cuprates in strong-coupling limit, distinct from BCS limit.
Tesanovic and Franz (Phys. Rev. B ’99, ‘03)
Strong phase fluctuations in d-wave superconductor treated by dual mapping
to Bosons in Hofstadter lattice --- vorticity and checkerboard pattern
Balents, Sachdev, Fisher et al. (2004)
Vorticity and checkerboard in underdoped regime
P. A. Lee, X. G. Wen. (PRL, ’03, PRB ’04)
Loss of phase coherence in tJ model, nature of vortex core
P. W. Anderson (cond-mat ‘05)
Spin-charge locking occurs at Tonset > Tc
Non-analytic magnetization
M vs H below Tc
Full Flux Exclusion
Strong Curvature!
-M
H
Hc1
Strong curvature persists above Tc
Anomalous high-temp. diamagnetic state
1.
Vortex-liquid state defined by large Nernst signal and
diamagnetism
2.
M(T,H) closely matched to eN(T,H) at high T (b is 103 - 104 times
larger than in ferromagnets).
3.
M vs. H curves show Hc2 stays v. large as T Tc.
4.
Magnetization evidence that transition is by loss of phase
coherence instead of vanishing of gap
5.
Nonlinear weak-field diamagnetism above Tc to Tonset.
6.
NOT seen in electron doped NdCeCuO (tied to pseudogap
physics)
End
Nernst effect in optimally doped YBCO
Nernst vs. H in optimally doped YBCO
Vortex onset temperature: 107 K
Relation between fluctuating M and Nernst current
Jy = ayx (-
T);
eN = raxy
Caroli Maki (‘69), Ussishkin, Sondhi (‘02)
axy = -b M
Fluctuating M generates a transverse charge flow in a gradient
Recently verified for vortices and ferromagnets
For vortices in Bi 2212, 1/b = 50-100 K
For ferromagnet spinel, 1/b = 105 K
Easy to distinguish between vortex flow and ferromagnetism
Temp. dependence of Nernst coef. in Bi 2201 (y = 0.60, 0.50).
Onset temperatures much higher than Tc0 (18 K, 26 K).
BCS transition
2D Kosterlitz Thouless transition
n vortex
D
D
r
s
0
r
s
Tc
H = ½ rs d3r ( )2
rs measures phase rigidity
0
TKT
TMF
Phase coherence destroyed at TKT
by proliferation of vortices
High temperature superconductors?
Plot of Hm, H*, Hc2 vs. T
• Hm and H* similar to
hole-doped
• However, Hc2 is
conventional
• Vortex-Nernst signal
vanishes just above Hc2
line
Isolated off-diagonal Peltier current axy versus T in LSCO
Vortex signal onsets at 50 and 100 K for x = 0.05 and 0.07