Vorticity and Phase Coherence
Download
1 / 82

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


  • 105 Views
  • Uploaded on

Vorticity and Phase Coherence in Cuprate Superconductors Yayu Wang, Lu Li, J. Checkelsky, N.P.O. Princeton Univ. M. J. Naughton, Boston College S. Uchida, Univ. Tokyo S. Ono, S. Komiya, Yoichi Ando, CRI, Elec. Power Inst., Tokyo Genda Gu , Brookhaven National Lab. Vortex Nernst effect

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Vortex Nernst effect Loss of long-range phase coherence The Upper Critical Field High-temperature Diamagnetism' - gasha


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Vorticity and Phase Coherence

in Cuprate Superconductors

Yayu Wang, Lu Li, J. Checkelsky, N.P.O. Princeton Univ.

M. J. Naughton, Boston College

S. Uchida, Univ. Tokyo

S. Ono, S. Komiya, Yoichi Ando, CRI,Elec. Power Inst., Tokyo

Genda Gu, Brookhaven National Lab

  • Vortex Nernst effect

  • Loss of long-range phase coherence

  • The Upper Critical Field

  • High-temperature Diamagnetism

Taipeh, June 2006


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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

LSCO = La2-xSrxCuO4

Bi 2212 = Bi2Sr2CaCu2O8

Bi 2201 = Bi2-yLaySr2CuO6


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Condensate described by a complex macroscopic wave function

Y(r) = Y1 + iY2 = |Y(r)| exp[iq(r)]

y2

y1

y2

y1

Anderson-Higgs mechanism: Phase stiffness

singular phase fluc. (excitation of vortices)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

q

q

q

q

q

q

Phase rigidity ruined by mobile defects

Long-range phase coherence requires uniform q

“kilometer of dirty lead wire”

phase rigidity measured by rs

Phase coherence destroyed by vortex motion

Kosterlitz Thouless transition in 2D films (1982)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

b(r)

Normal core

Js

x

x

b(r)

|Y| = D

London length l

Vortices, fundamental excitation of type-II SC

Vortex in cuprates

Vortex in Niobium

CuO2 layers

superfluid

electrons

Js

2D vortex pancake

H

coherence length x



Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

normal

liquid

Hm

Hc2

vortex solid

Hc1

0

Tc0

T

Mean-field phase diagram

Cuprate phase diagram

2H-NbSe2

4 T

100 T

Hc2

H

H

vortex

liquid

Hm

Tc

vortex

solid

100 K

7 K

Meissner state


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Vortex signal persists to 70 K above Tc.

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Wang, Li, Ong PRB 2006

Vortex-Nernst signal in Bi 2201


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Nernst signal

eN = Ey /| T |

Nernst curves in Bi 2201

Yayu Wang,Lu Li,NPO PRB 2006

underdoped

optimal

overdoped


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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?


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Nernst

region

  • Loss of phase coherence determines Tc

  • Condensate amplitude persists T>Tc

  • Vorticity and diamagnetism in Nernst region


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

In hole-doped cuprates

  • Existence of vortex Nernst signal above Tc

  • Confined to superconducting “dome”

  • Upper critical field Hc2 versus T is anomalous

  • Loss of long-range phase coherence at Tc

  • by spontaneous vortex creation (not gap closing)

  • 5. Pseudogap intimately related to vortex liquid state

More direct (thermodynamic) evidence?


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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

Diamagnetic currents in vortex liquid

Supercurrents follow contours of condensate


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

×

B

m

Cantilever torque magnetometry

Torque on magnetic moment:  = m × B

crystal

Deflection of cantilever:  = k 


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Micro-fabricated single crystal silicon cantilever magnetometer

H

  • Capacitive detection of deflection

  • Sensitivity: ~ 5 × 10-9 emu at 10 tesla

  • ~100 times more sensitive than commercial SQUID


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Underdoped

Bi 2212

Wang et al.

Cond-mat/05

Tc



Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Magnetization curves in underdoped Bi 2212

Wang et al.

Cond-mat/05

Tc

Separatrix Ts


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

y2

y1

y2

y1

Anderson-Higgs mechanism: Phase stiffness

singular phase fluc. (excitation of vortices)



Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

M(T,H) matches eN in both H and T above Tc


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Wang et al.

Cond-mat/05


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

normal

liquid

Hm

Hc2

vortex solid

Hc1

0

Tc0

T

Mean-field phase diagram

Cuprate phase diagram

2H-NbSe2

4 T

100 T

Hc2

H

H

vortex

liquid

Hm

Tc

vortex

solid

100 K

7 K

Meissner state


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Electron-doped optimal

Hole-doped optimal

Tc

Tc


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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

TemperatureT

vortex liquid

Tc

superfluidity

long-range phase coherence

Meissner eff.

0

x (holes)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

  • In hole-doped cuprates

  • 1. Large region in phase diagram above Tc dome

  • with enhanced Nernst signal

  • Associated with vortex excitations

  • Confirmed by torque magnetometry

  • Transition at Tc is 3D version of KT transition

  • (loss of phase coherence)

  • 5. Upper critical field behavior confirms conclusion



Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

x

+

o

-

-

x (A)

+

Hc2

4 Tesla

40

10

100 Tesla

Cooper pairing in cuprates

d-wave symmetry

coherence length

Upper critical field

cuprates

NbSe2

MgB2

Nb3Sn

57

18

29

90


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Contrast with Gaussian (amplitude) fluctuations

In low Tc superconductors,

Evanescent droplets of

superfluid radius x

exist above Tc

x

At Tc, (Schmidt, Prange ‘69)

M’ = 2p1/2(kBTc / f03/2) B1/2

This is 30-50 times smaller than observed in Bi 2212


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

“Fluctuation diamagnetism” distinct from Gaussian fluc.

Wang et al. PRL 2005

1. Robustness

Survives to H > 45 T.

Strongly enhanced by field.

(Gaussian fluc. easily suppr. in H).

2.Scaling with Nernst

Above Tc, magnetization M

scales as eN vs. H and T.

3. Upper critical field

Behavior of Hc2(T) not mean-field.


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

+

-

-

+

Hc2

vortex

liquid

Hm

Tc

Signature features of cuprate superconductivity

1. Strong Correlation

2. Quasi-2D anisotropy

3. d-wave pairing, very short x

4. Spin gap, spin-pairing at T*

5. Strong fluctuations, vorticity

6. Loss of phase coherence at Tc


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Comparison between x = 0.055 and 0.060

Sharp change in ground state

Lu Li et al., unpubl.

Pinning current reduced by a factor of ~100 in ground state


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Two distinct field scales

In ground state, have 2 field scales

1) Hm(0) ~ 6 T

Dictates phase coherence, flux expulsion

2) Hc2(0) ~ 50 T

Depairing field. Scale of condensate suppression

M (A/m)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Magnetization in lightly doped La2-xSrxCuO4

Lu Li et al., unpubl.

SC dome

0.03

0.05

0.04

0.06

4.2 K

5 K

5 K

30 K

35 K

30 K

35 K

4.2 K


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Vortex-liquid boundary linear in x as x 0?

dissipative,

vortices mobile

Long-range

phase coherence

Sharp transition in Tc vs x (QCT?)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

The case against inhomogeneous superconductivity

(granular Al)

  • LaSrCuO transition at T = 0 much too sharp

  • Direct evidence for competition between d-wave SC

  • and emergent spin order

  • 3. In LSCO, Hc2(0) varies with x


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

  • Abrupt transition between different ground states

  • at xc = 0.055

  • 1. Phase-coherent ground state (x > 0.055)

  • Cooling establishes vortex-solid phase; sharp melting field

  • 2. Unusual spin-ordered state (x < 0.055)

  • i) Strong competition between diamagnetic state

  • and paramagnetic spin ordering

  • ii) Diamagnetic fluctuations extend to x = 0.03

  • iii) Pair condensate robust to high fields (Hc2~ 20-40 T)

  • iv) Cooling to 0.5 K tips balance against phase coherence.

Competing ground states


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Field sensitivity of Gaussian fluctuations

Gollub, Beasley,

Tinkham et al.

PRB (1973)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Vortex signal above Tc0 in under- and over-doped Bi 2212

Wang et al. PRB (2001)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

x

Abrikosov vortices near Hc2

Upper critical fieldHc2 = f0/2px2

Condensate destroyed when cores touch at Hc2


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

  • 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)



Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Tc

110K

  • In underdoped Bi-2212, onset of diamagnetic fluctuations at 110 K

  • diamagnetic signal closely tracks the Nernst effect


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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

Wang et al. Science (2003)



Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

4 T

normal

?

?

liquid

vortex

liquid

H

Hm

Hc2

vortex solid

vortex

solid

Hm

Hc1

Hc1

0

Tc0

0

Tc0

T

T

Phase diagram of type-II superconductor

cuprates

2H-NbSe2

H

Meissner state


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

x

Gap D

Tc

Temp. T

Superconductivity in low-Tc superconductors (MF)

Cooper pairs with coherence length x

Quasi-particles

Energy gap D

Pairs obey macroscopic wave function

Phase

amplitude

Phase q important in Josephson effect


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

c, z

H

q

mp

M

t

mp

H

M

Torque magnetometry

Van Vleck (orbital) moment mp

t= mpx B + MV x B

2D supercurrent

t/V = ccHx Bz – caHz Bx + M Bx

Meff = t / VBx = DcpHz + M(Hz)

Exquisite sensitivity to 2D supercurrents


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Wang et al., unpublished

Hc2(0) vs x matches Tonset vs x


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Tco

Overdoped LaSrCuO x = 0.20

H*

Hm


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

-M

H

M vs H below Tc

Full Flux Exclusion

Strong Curvature!

Hc1




Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Susceptibility and Correlation Length

Strongly H-dependent

Susceptibility c = M/H

Fit to

Kosterlitz Thouless theory

c = -(kBT/2df02) xKT2

xKT = a exp(b/t1/2)


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Non-analytic magnetization above Tc

M ~ H1/d

Fractional-exponent

region


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Wang et al. Science (2003)

overdoped

optimum

underdoped

Field scale increases as x decreases



Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Xu et al. Nature (2000)

Wang et al. PRB (2001)

Nernst effect in LSCO-0.12

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

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

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Resistivity is a 0.50).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.


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Bardeen Stephen law (not seen) 0.50).

Resistivity Folly

Ong Wang, M2S-RIO, Physica C (2004)

Hc2

Hc2

Resistivity does not distinguish vortex liquid from normal state


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Isolated off-diagonal Peltier current 0.50).axy versus T in LSCO

Vortex signal onsets at 50 and 100 K for x = 0.05 and 0.07


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

T 0.50).co

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


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Nernst effect in optimally doped YBCO 0.50).

Vortex onset temperature: 107 K

Nernst vs. H in optimally doped YBCO


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Separatrix curve at T 0.50).s

Optimum doped

Overdoped


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Vortex Nernst signal 0.50).

axy = b M

b-1 = 100 K


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

n 0.50).

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?


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Strong correlation in CuO 0.50).2 plane

Cu2+

Large U

charge-transfer

gap Dpd ~ 2 eV

best evidence

for large U

metal?

Mott insulator

antiferromagnet

J~1400 K

doping

Hubbard

t = 0.3 eV, U = 2 eV, J = 4t2/U = 0.12 eV


Vortex nernst effect loss of long range phase coherence the upper critical field high temperature diamagnetism

Electron-doped optimal 0.50).

Hole-doped optimal