Transcript Vortex-Nernst signal and extended phase diagram of cuprates Yayu Wang, Z.

Vortex-Nernst signal and extended phase diagram of cuprates
Yayu Wang, Z. A. Xu, N.P.O (Princeton)
T. Kakeshita, S. Uchida (U. Tokyo)
S. Ono and Y. Ando (CRIEPI, Japan)
D. A. Bonn, R. Liang, W.N. Hardy (U. Brit. Colum.)
G. Gu (Brookhaven Nat. Lab.)
B. Keimer (MPI, Stuttgart)
Y. Onose and Y. Tokura (U. Tokyo)
1.
Vortex Nernst signal above Tc
2.
The extended phase diagram to high fields
3.
Upper critical field problem
4.
Variation of Hc2 vs. x
LaSrCuO
YBaCuO
Bi 2201
Bi 2212
Bi 2223
NdCeCuO …
High-fields at NHMFL, Tallahassee
Supported by NSF, ONR and NEDO
Phase diagram of type II superconductor
cuprates
2H-NbSe2
normal
?
?
liquid
Hm
vortex
liquid
H
Hc2
vortex solid
H
vortex
solid
Hc1
0
Hc1
Tc0
T
0
Upper critical field Hc2 = f0/2px02
Hc2
coherence length x0
Hm
T
Tc0
Nernst experiment
Vortices move in a temperature gradient
Phase slip generates Josephson voltage
2eVJ = 2ph nV
EJ = B x v
Nernst signal
ey = Ey / | T |
Nernst coefficient
v = ey / B
Nernst signal versus field at fixed T in LaSrCuO (x = 0.12)
Bi2Sr2-yLayCu2O6
Tc = 28 K
Nernst signal survives up to 80 K
Vortex signal above Tc0 in under- and over-doped Bi 2212
•
Nernst signal extends
up to Tonset ~ T*/2
•
Vanishing of phase
coherence at Tc0
(RVB, Baskaran et al.,
’87
Kivelson, Emery ‘95)
•
Pseudogap state nearly
degenerate with dSC
•
Strong fluctuations
between the two states
T*
0
Ridge field H*(T)
Tco
Contour plot of Nernst signal ey in T-H plane
• Vortex signal extends above Tc0 continuously
As x increases, vortex-liquid regime shrinks rapidly,
Hm(T) moves towards H*(T).
Where is Hc2 line?
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
• Upper critical Field Hc2 given by ey
0
10
20
30
m 0 H (T)
0.
• Hole cuprates --- Need intense fields.
40
50
60
Nernst signal in overdoped Bi 2201 in fields up to 45 Tesla
Nernst signal ey in overdoped LaSrCuO
ey attains a T-dept.
maximum, and goes
to 0 at large H.
By extrapolation,
Hc2(0) ~ 50 Tesla.
Nernst signal ey in PbIn.
• Three field scales
Hm(T), H*(T), and
Hc2(T).
H*
• Hc2 vs. T curve
does not terminate at
Tc0 (remains large)
Phase coherence lost at
Tc0 but D is finite
Hm
Tco
Contour plots in
underdoped YBaCuO6.50
(main panel) and optimal
YBCO6.99 (inset).
• Vortex signal extends above
70 K in underdoped YBCO,
to 100 K in optimal YBCO
• High-temp phase merges
continuously with vortex
liquid state
Tco
Vortex-Nernst signal in Nd2-xCexCuO4 (x = 0.15)
• Hc2 determined by ey
• H* fixed by peak in ey
• ey vanishes above Tc0
(unlike in hole doped)
0
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
NbSe2
Hole-doped cuprates
NdCeCuO
Hc2
Hc2
Hc2
Hm
Hm
Hm
Tc0
‘Conventional’
Amplitude transition
at Tc0 (BCS)
Tc0
Expanded vortex liquid
Amplitude trans. at Tc0
Tc0
Vortex liquid phase is
dominant.
Loss of phase coherence
at Tc0 (zero-field melting)
optimum
overdoped
underdoped
3.5
OD-Bi2212 ( T c =65K)
3.0
50
OPT-Bi2212 ( T c =90K)
45
3.0
70K
3.0
55
50
90
1.5
85
1.5
25
65
60
1.0
65
95
0.5
75
0.0
10
1.0
1.5
70
70
5
55
2.0
30
0
2.0
80
60
0.5
40K
45
2.5
2.5
35
2.0
1.0
UD-Bi2212 ( T c =50K)
75
40
2.5
e y (m V/K)
3.5
15
m 0 H (T)
20
25
20
80
85 0.0
90
30
0
0.5
100
105
110
5
10
15
0.0
20
25
30
0
m 0 H (T)
Field scale increases as x decreases
5
10
75
80
90
100
15
20
m 0 H (T)
25
30
Vortex-Nernst signal in single-layer Bi 2201
Scaling of ey near Tc0
• Curves at Tc0 obey scaling behavior ey/eymax = F(h)
• Allows Hc2(Tc0) to be determined.
Hc2 and D0 vs. x in Bi 2212
Coherence length vs. x
This work
STM
ARPES
• Hc2 increases as x decreases (like ARPES gap D0)
• Compare xH (from Hc2) with
Pippard length x0 = hvF/aD0 (a = 3/2)
STM vortex core xSTM ~ 22 A
Feng et al. Science, 99
Ding et al. PRL 2001
Hudson et al. PRL 2001
Implications of Hc2 vs. x
Pair potential
rs
• Pair potential largest in underdoped
(RVB theory, … Baskaran ‘87)
• Loss of phase coherence fixes Tc0
(Emery Kivelson 1995)
?
Tc0
x
• Tc0 suppression at 0.05 not driven
by competing order?
Resistivity is a bad diagnostic for field
suppression of pairing amplitude
Plot of r and ey versus T at fixed H
(33 T).
Vortex signal is large for T < 26 K,
but r is close to normal value rN
above 15 K.
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
Summary
1. Vortex Nernst signal above Tc
in LaSrCuO, YBaCuO, Bi 2201, Bi
2212, Bi 2223, NdCeCuO….
2. Contour plots of ey
Smooth continuity between incoherent
vortex regime and vortex liquid
3. Hc2 determined in overdoped regime
Hc2(0) = 50 T for x = 0.20 in LSCO
Hc2 vs. T does not terminate at Tc0
Phase coherence lost at Tc0
but Hc2 and D are finite
4. Hc2 vs. x determined from scaling.
Hc2 largest in underdoped regime
Appendix
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
Line entropy sf vs. H in LaSrCuO
sf = f0 ey/r.
At large H, sf goes
to zero linearly.
Intercept gives
Hc2(T).
Optimal, untwinned BZO-grown YBCO
sf = “transport line-entropy” of vortex
gradient
fT = -sf
friction
-hv
Ey = Bvx
-hv
-sf T
T
- T
ey = Bsf/h = sfr/f0
sf= f0 ey/r
|M|
Tsf = f0 |M(T,H)| LD(T)
sf
near Hc2 line (Caroli Maki ’68)
0
H
Hc2
Underdoped
Overdoped
Nernst signal in underdoped YBaCuO (Tc = 50 K)
and overdoped LaSrCuO (Tc = 29 K).
Intrinsic field scale much higher in underdoped YBCO.
Nernst signal in overdoped LSCO and Bi 2212
4
0
5
10
15
20
160
5
t=1.0
4
120
3
2
2
m 0H c2 (T)
e y (m V/K)
3
100
80
60
40
1
Bi-2201 (La:0.6)-18K
1
Bi-2201 (La:0.4)-28K
0
Bi-2212
Bi-2201
140
0
2
4
6
8
10
12
0
14
m 0 H (T)
Similar trend in Bi-2201
20
0
0.05
0.10
0.15
x
0.20
0.25
A new length scale x*
x0
Cheap, fat vortices
x0
D(r)
Js(r)
Js(r)
0
0
f0
H* =
2px*2
Is H* determined by
close-packing of fat vortices?
D(r)
x*
Temp. dependence of Nernst coef. in Bi 2201 (y = 0.60, 0.50).
Onset temperatures much higher than Tc0 (18 K, 26 K).
Diffusion of vortices produces
Josephson E-field
z
E= Bxv
x
V
.E
H
y
Charge currents in normal
state (top view):
J = s.E and J’ = a.(-dT)
Nernst signal very small
x
Ettinghausen-Nernst signal in PbIn (Tc = 7.1 K)
ey peaks within vortex state.
sf linear in (Hc2- H) near Hc2.
Caroli-Maki
Tsf = f0 |M(T,H)| LD(T)