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Vortex Nernst effect Loss of long-range phase coherence The Upper Critical Field High-temperature Diamagnetism KT vs 3DX PowerPoint Presentation
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Vortex Nernst effect Loss of long-range phase coherence The Upper Critical Field High-temperature Diamagnetism KT vs 3DX - PowerPoint PPT Presentation


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What lies above : the vortex liquid above T c in cuprate superconductors. Yayu Wang, LuLi, J. Checkelsky, N.P.O. Princeton Univ. M. J. Naughton, Boston College. Vortex Nernst effect Loss of long-range phase coherence The Upper Critical Field High-temperature Diamagnetism

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slide1

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

  • 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

slide2

Mott insulator

T*

T

pseudogap

Tc

Fermi

liquid

AF

dSC

0

0.25

0.05

doping x

Phase diagram of Cuprates

s = 1/2

hole

slide3

b(r)

Normal core

Js

x

x

Vortex in cuprates

Vortex in Niobium

CuO2 layers

superfluid

electrons

Js

H

2D vortex pancake

Gap D(r) vanishes in core

|Y| = D

slide4

Phase difference

vortex

2p

f

Integrate VJ to give dc signal

prop. to nv

VJ

t

The Josephson Effect, phase-slippage and Nernst signal

Passage of a vortex

Phase diff. f jumps by 2p

slide5

Nernst signal

ey = Ey /| T |

Vortices move in a temperature gradient

Phase slip generates Josephson voltage

2eVJ = 2ph nV

EJ = B x v

Nernst experiment

ey

Hm

H

slide6

Nernst effect in underdoped LSCO-0.12 with Tc = 29K

vortex Nernst signal onset from T = 120 K, ~ 90K above Tc`1

slide7

Vortex signal persists to 70 K above Tc !

Nernst effect in underdoped Bi-2212 (Tc = 50 K)

slide10

q

q

q

q

q

q

Phase rigidity

|Y| eiq(r)

Long-range phase coherence requires uniform q

“kilometer of dirty lead wire”

phase rigidity measured by rs

Phase coherence destroyed by vortex motion

Emery, Kivelson, (1995): Spontaneous vortex creation at Tc in cuprates

slide11

rs

D

0

TKT

TcMF

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 vortices appear spontaneously

3D version of KT transition in cuprates?

slide12

Loss of phase coherence determines Tc

  • Condensate amplitude persists T>Tc
slide13

overdoped

optimum

underdoped

Field scale increases as x decreases

slide14

T=1.5K

T=8K

Hd

Hc2

0.3

1.0

H/Hc2

  • Upper critical Field Hc2 given by ey 0.
  • Hole cuprates --- Need intense fields.

PbIn, Tc = 7.2 K (Vidal, PRB ’73)

Bi 2201 (Tc= 28 K, Hc2 ~ 48 T)

ey

Hc2

slide16

Hc2increases 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

LSCO

D

D0 (Ding)

Cooper pairing potential largest in underdoped regime

slide17

Hole-doped cuprates

NbSe2

NdCeCuO

Hc2

Hc2

Hc2

vortex

liquid

vortex

liquid

Hm

Hm

Hm

Tc0

Tc0

Tc0

Vortex liquid dominant.

Loss of phase coherence

at Tc0 (zero-field melting)

Expanded vortex liquid

Amplitude vanishes at Tc0

Conventional SC

Amplitude vanishes

at Tc0 (BCS)

slide18

Js = -(eh/m) x |Y|2 z

Diamagnetic currents in vortex liquid

H

Supercurrents follow contours of condensate

slide19

×

B

m

Cantilever torque magnetometry

Torque on magnetic moment:  = m × B

crystal

Deflection of cantilever:  = k 

slide20

Micro-fabricated Si single-crystal cantilever

  • Very thin cantilever beam: ~ 5 m

Micro-fabricated single crystal silicon cantilever magnetometer(Mike Naughton)

H

  • Capacitive detection of deflection
  • Sensitivity: ~ 5 × 10-9 emu at 10 tesla
  • ~200 times more sensitive than commercial SQUID
slide23

Tc

110K

  • In underdoped Bi-2212, onset of diamagnetic fluctuations at 110 K
  • diamagnetic signal closely tracks the Nernst effect
slide28

Magnetization in Abrikosov state

M

H

Hc1

Hc2

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

slide31

Hc2

Hc2

M

T Tc-

Tc

In conventional type II supercond., Hc2 0

Hc2

Hc2

M

Tc

In cuprates, Hc2 is unchanged as T Tc

slide33

Bardeen Stephen law (not seen)

Resistivity Folly

Hc2

Hc2

Resistivity does not distinguish vortex liquid and normal state

slide34

Phase fluctuation in cuprate phase diagram

spin pairing

(NMR relaxation,

Bulk suscept.)

T*

pseudogap

Tonset

Onset of charge pairing

Vortex-Nernst signal

Enhanced diamagnetism

Kinetic inductance

Temperature T

vortex liquid

Tc

superfluidity

long-range phase coherence

Meissner eff.

0

x (holes)

slide35

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

slide37

-M

H

M vs H below Tc

Full Flux Exclusion

Strong Curvature!

Hc1

slide39

Anomalous high-temp. diamagnetic state

  • Vortex-liquid state defined by large Nernst signal and diamagnetism
  • M(T,H) closely matched to eN(T,H) at high T (b is 103 - 104 times larger than in ferromagnets).
  • M vs. H curves show Hc2 stays v. large as T Tc.
  • Magnetization evidence that transition is by loss of phase coherence instead of vanishing of gap
  • Nonlinear weak-field diamagnetism above Tc to Tonset.
  • NOT seen in electron doped NdCeCuO (tied to pseudogap physics)
slide41

Nernst effect in optimally doped YBCO

Vortex onset temperature: 107 K

Nernst vs. H in optimally doped YBCO

slide42

Jy = ayx (- T); eN = raxy

Relation between fluctuating M and Nernst current

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

slide43

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

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

slide44

n

vortex

D

0

T

T

T

c

KT

MF

H = ½rsd3r ( f)2

r

r

s

s

2D Kosterlitz Thouless transition

BCS transition

D

0

Phase coherence destroyed at TKT

by proliferation of vortices

rs measures phase rigidity

High temperature superconductors?

slide45

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
slide46

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