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

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

Nernst experiment

Vortices move in a temperature gradientPhase slip generates Josephson voltage

2eVJ = 2h nV

EJ = B x v

Nernst signal versus field at fixed T in LaSrCuO (x = 0.12)

Nernst signal

ey = Ey / | T |

Nernst coefficient

v = ey / B

Bi2Sr2-yLayCu2O6 Tc = 28 KNernst 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., ’87Kivelson, Emery ‘95)

• Pseudogap state nearly degenerate with dSC

• Strong fluctuations between the two states

T*

0

Contour plot of Nernst signal ey in T-H plane

• Vortex signal extends above Tc0 continuously

Tco

Ridge field H*(T)

As x increases, vortex-liquid regime shrinks rapidly,Hm(T) moves towards H*(T).

Where is Hc2 line?

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.

Nernst signal in overdoped Bi 2201 in fields up to 45 Tesla

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.

• 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

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

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)

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 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)

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

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 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

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

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.

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

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

Appendix

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

s = ey/

At large H, s goes to zero linearly.

Intercept gives Hc2(T).

Line entropy s vs. H in LaSrCuO

Optimal, untwinned BZO-grown YBCO

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

Nernst signal in underdoped YBaCuO (Tc = 50 K) and overdoped LaSrCuO (Tc = 29 K).Intrinsic field scale much higher in underdoped YBCO.

Underdoped Overdoped

Nernst signal in overdoped LSCO and Bi 2212

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

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?

*

Temp. dependence of Nernst coef. in Bi 2201 (y = 0.60, 0.50).

Onset temperatures much higher than Tc0 (18 K, 26 K).

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

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)