Vortex-Nernst signal and extended phase diagram of cuprates
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Transcript of Vortex-Nernst signal and extended phase diagram of cuprates
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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
LaSrCuOYBaCuOBi 2201Bi 2212Bi 2223NdCeCuO …
High-fields at NHMFL, TallahasseeSupported by NSF, ONR and NEDO
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Phase diagram of type II superconductor
H
T
Hc2
Hc1
Tc0
normal
vortex solid
liquid
0
Hm
2H-NbSe2cuprates
vortex solid
vortexliquid
??
Hm
0 T Tc0
H
Hc1
Upper critical field Hc2 = 0/22
Hc2 coherence length
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Nernst experiment
Vortices move in a temperature gradientPhase slip generates Josephson voltage
2eVJ = 2h nV
EJ = B x v
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Nernst signal versus field at fixed T in LaSrCuO (x = 0.12)
Nernst signal
ey = Ey / | T |
Nernst coefficient
v = ey / B
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Bi2Sr2-yLayCu2O6 Tc = 28 KNernst signal survives up to 80 K
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Vortex signal above Tc0 in under- and over-doped Bi 2212
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• Nernst signal extends up to Tonset ~ T*/2
• Vanishing of phase coherence at Tc0
(RVB, Baskaran et al., ’87Kivelson, Emery ‘95)
• Pseudogap state nearly degenerate with dSC
• Strong fluctuations between the two states
T*
0
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Contour plot of Nernst signal ey in T-H plane
• Vortex signal extends above Tc0 continuously
Tco
Ridge field H*(T)
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As x increases, vortex-liquid regime shrinks rapidly,Hm(T) moves towards H*(T).
Where is Hc2 line?
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ey
PbIn, Tc = 7.2 K (Vidal, PRB ’73) Bi 2201 (Tc = 28 K, Hc2 ~ 48 T)
0 10 20 30 40 50 600.0
0.5
1.0
1.5
2.0
ey (V
/K)
0H (T)
T=8K
Hc2
T=1.5K
Hd
0.3 1.0H/Hc2
Hc2
• Upper critical Field Hc2 given by ey 0.
• Hole cuprates --- Need intense fields.
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Nernst signal in overdoped Bi 2201 in fields up to 45 Tesla
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ey attains a T-dept. maximum, and goes to 0 at large H.
By extrapolation,
Hc2(0) ~ 50 Tesla.
Nernst signal ey in overdoped LaSrCuO
Nernst signal ey in PbIn.
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• Three field scalesHm(T), H*(T), and Hc2(T).
• Hc2 vs. T curve does not terminate at Tc0 (remains large)
H*
Hm
Phase coherence lost at Tc0 but is finite
Tco
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Contour plots in underdoped YBaCuO6.50 (main panel) and optimalYBCO6.99 (inset).
Tco
• Vortex signal extends above70 K in underdoped YBCO,to 100 K in optimal YBCO
• High-temp phase merges continuously with vortex liquid state
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Vortex-Nernst signal in Nd2-xCexCuO4 (x = 0.15)
• Hc2 determined by ey 0
• H* fixed by peak in ey
• ey vanishes above Tc0
(unlike in hole doped)
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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
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NbSe2 NdCeCuO Hole-doped cuprates
Tc0 Tc0Tc0
Hc2 Hc2Hc2
Hm
HmHm
‘Conventional’Amplitude transitionat Tc0 (BCS)
Expanded vortex liquid Amplitude trans. at Tc0
Vortex liquid phase is dominant.Loss of phase coherenceat Tc0 (zero-field melting)
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0 5 10 15 20 25 300.0
0.5
1.0
1.5
2.0
2.5
3.0
100908075
65
60
55
50
45
70
40KUD-Bi2212 (T
c=50K)
0H (T)
0 5 10 15 20 25 30
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
908580
75
70
65
60
55
5045
40
35
30
25
20
OD-Bi2212 (Tc=65K)
ey (V
/K)
0H (T)
Field scale increases as x decreases
0 5 10 15 20 25 30
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
105110
9085
80
75
95
100
70K
OPT-Bi2212 (Tc=90K)
0H (T)
overdoped optimum underdoped
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Vortex-Nernst signal in single-layer Bi 2201
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Scaling of ey near Tc0
• Curves at Tc0 obey scaling behavior ey/eymax = F(h)
• Allows Hc2(Tc0) to be determined.
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Hc2 and vs. x in Bi 2212 Coherence length vs. x
Feng et al. Science, 99Ding et al. PRL 2001Hudson et al. PRL 2001
STM
This work
ARPES
• Hc2 increases as x decreases (like ARPES gap 0)
• Compare H (from Hc2) with
Pippard length 0 = hvF/0 ( = 3/2)STM vortex core STM ~ 22 A
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Implications of Hc2 vs. x
• Pair potential largest in underdoped(RVB theory, … Baskaran ‘87)
• Loss of phase coherence fixes Tc0 (Emery Kivelson 1995)
• Tc0 suppression at 0.05 not driven by competing order?
s
Pair potential
Tc0
x
?
s
Pair potential
Tc0
x
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Resistivity is a bad diagnostic for field suppression of pairing amplitude
Plot of and ey versus T at fixed H (33 T).
Vortex signal is large for T < 26 K, but is close to normal value N
above 15 K.
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0 2 4 6 8 10 12 140.0
0.2
0.4
0.6
0.8
ey
12K
NdCCO (T
c=24.5K)
ey (V
/K)
0H (T)
0 5 10 15 20 25 300.0
0.2
0.4
0.6
0.8
1.0
22K
ey
LSCO (0.20)
ey(
V/K
)
0H (T)
Resistivity does not distinguish vortex liquid and normal state
Hc2Hc2
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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 are finite
4. Hc2 vs. x determined from scaling.Hc2 largest in underdoped regime
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Appendix
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Isolated off-diagonal Peltier current xy versus T in LSCO
Vortex signal onsets at 50 and 100 K for x = 0.05 and 0.07
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s = ey/
At large H, s goes to zero linearly.
Intercept gives Hc2(T).
Line entropy s vs. H in LaSrCuO
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Optimal, untwinned BZO-grown YBCO
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Ey = Bvxey = Bs/ = s
s= ey/
s = “transport line-entropy” of vortex
Ts = |M(T,H)| LD(T)
near Hc2 line (Caroli Maki ’68)
v
H Hc2
|M|
s
0
gradient fT = -s T
- Tfriction -v
-s T
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Nernst signal in underdoped YBaCuO (Tc = 50 K) and overdoped LaSrCuO (Tc = 29 K).Intrinsic field scale much higher in underdoped YBCO.
Underdoped Overdoped
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Nernst signal in overdoped LSCO and Bi 2212
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0 2 4 6 8 10 12 140
1
2
3
40 5 10 15 20
0
1
2
3
4
5
t=1.0
ey (V
/K)
0H (T)
Bi-2201 (La:0.6)-18K
Bi-2201 (La:0.4)-28K
0.05 0.10 0.15 0.20 0.250
20
40
60
80
100
120
140
160
Bi-2212 Bi-2201
0H
c2 (
T)
x
Similar trend in Bi-2201
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A new length scale * Cheap, fat vortices
0
Js(r)
(r) (r)
Js(r)
0
00
H* = 0
2*2
Is H* determined byclose-packing of fat vortices?
*
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Temp. dependence of Nernst coef. in Bi 2201 (y = 0.60, 0.50).
Onset temperatures much higher than Tc0 (18 K, 26 K).
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Charge currents in normalstate (top view):J = .E and J’ = .(-
Nernst signal very small
H
x
y
. E
V
x
z
Diffusion of vortices producesJosephson E-field
E = B x v
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ey peaks within vortex state.
s linear in (Hc2- H) near Hc2.
Caroli-MakiTs = |M(T,H)| LD(T)
Ettinghausen-Nernst signal in PbIn (Tc = 7.1 K)
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