1. Introduction2. Vortex Nernst effect3. Enhanced Diamagnetism4. Fragile London rigidity T>Tc5. Low-temp. Quantum Vortex Liquid State

Vorticity and the Phase Diagram of Cuprates

Lu Li, J. G. Checkelsky, N.P.O. Princeton Univ.Yayu Wang, Princeton U., U.C. Berkeley

M. J. Naughton, Boston CollegeS. Ono, S. Komiya, Yoichi Ando, CRI, Elec. Power Inst., Tokyo

S. Uchida, Univ. Tokyo Genda Gu, Brookhaven National Lab

Hong Kong Univ, Dec. 2006

1. (1975-80) Sliding charge density waves (LRA)Pinning and Depinning, FLR length

2. (1980-84) Gang of four, weak localization, Magnetoresistance, dephasing

3. (1987-2000)RVB and Gauge theories of cuprate pairing (NL, WL)

4. (1995-98)Thermal conductivity of Dirac quasiparticlesThermal Hall effect and qp-vortex scattering

5. (2000 -- )Strong fluctuations in pseudogap state

BC

AD

Thanks, Patrick!

holes = 1/2

Phase diagram of cuprates

T pseudogap

0 0.05 0.25

T*

Tc

Mott insulator

Fermiliquid

doping x (fraction of sites with holes)

vortex liquid

dSCAF

Spontaneous vorticity destroys superfluidity

Josephson Effect, phase-slip and Nernst signal

t

VJ

2

Ph

ase

dif

fere

nce

Passage of a vortex Phase diff. jumps by 2

Integrate VJ to give dc signalprop. to nv

JeV2 = 2h nV

Josephson Eq.

Nernst effect experiment

Vortices move in a temperature gradientPhase slip generates Josephson voltage

2eVJ = 2h nV

EJ = B x v

ey = Ey /| T | (Nernst signal)

Tc

Nernst signal persists highabove Tc

Bi 2212 (UD)

Wang et al. PRB 2001

Giant Nernst signal in cuprates

overdoped optimal underdoped

Wang, Li, NPO PRB 2006

Nernst signal

eN = Ey /| T |

Vortex-Nernst signal in Bi 2201 Wang, Li, Ong PRB 2006

• Condensate amplitude persists to Tonset > Tc

• Nernst signal confined to SC dome• Vorticity defines Nernst region

Nernstregion

Kosterlitz Thouless transition in 2D superconductor

Unbinding ofvortex-antivortex

F = U - TSFree energy gain

vortex density

vortex

antivortex

Mean-field phase diagram

H

2H-NbSe2

T

Hc2

Hc1

Tc0

normal

vortex solid

liquid

0

Hm

Meissner state

H

Cuprate phase diagram

4 T

7 Kvortexsolid

vortexliquid

Hc2

Tc

100 T

100 K

Hm

Vortex unbindingin H = 0

1. Vorticity persists high above Tc

2. Confined to SC “dome”

3. Loss of long-range phase coherence at Tc by spontaneous vortex creation (not gap closing)

4. Pseudogap intimately related to vortex liquid state

Thermodynamic evidence?

Implications of Giant Nernst signal

Supercurrents follow contours of condensate

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

Diamagnetic currents in vortex liquid

Torque magnetometry

Torque on moment: = m × B

Deflection of cantilever: = k

crystal

B

m×

Mike Naughton (Boston College)

Tc

UnderdopedBi 2212

Wang et al.PRL 2005

Magnetization curves in underdoped Bi 2212

Tc

Separatrix Ts

Wang et al.Cond-mat/05

Wang et al.PRL 2005

At high T, M scales with Nernst signal eN

Lu Li et al., unpubl.HM

M = - [Hc2 – H] / (22 –1)

Hc2

UN Bi 2212

“Fragile” London rigidity above Tc

Above Tc, M/H is singularM ~ -H1/is divergent)

Lu Li et al. Europhys Lett 2005

Non-analytic magnetization above Tc

M ~ H1/

Fractional-exponentregion

In hole-doped cuprates

1. Large region in phase diagram above Tc domewith enhanced Nernst signal

2. Associated with vortex excitations (not Gaussian)

3. Confirmed by torque magnetometry

4. Transition at Tc is 3D version of KT transition (loss of phase coherence)

5. Upper critical field behavior confirms conclusion

Nernstregion

The phase diagramin x-H plane at low T

H

x0 0.30.1 0.2

?

Magnetization in lightly doped La2-xSrxCuO4

Lu Li et al., unpubl.

Evidence for robust diagmagnetism for x < xc

Lu Li et al., unpubl.

Diamagnetism coexists with growing spin population

Doping x

Lu Li et al., unpubl.

Debye Waller dependence Hm(T) = H0 exp(-T/T0)

Vortex solid-to-liquid transition for x < xc

Lu Li et al., unpubl.Low temp Phase Diagram

Critical Point

H

x0 0.30.1 0.2

Low-temperature vortex liquid

1. Vortex solid surrounded by vortex liquid at 0.35 K

2. Sharp quantum transition at xc = 0.055. Quantum vortices destroy phase coherence

3. At 0.35 K, pair condensate survives without phase rigidity even for x = 0.03

4. Melting of vortex solid appears to be classical at 0.35 K (Debye-Waller like).

Summary

1. Nernst region is suffused with vorticity, enhanced diamagnetism and finite pairing amplitude

2. Extends from Tc to Tonset < T*

3. Nernst region dominates lower temp part ofPseudogap state

4. Depairing field Hc2 and binding energy arevery large

Strong pairing potential but soft phase rigidity

5. Vortex-liquid state is ground state below xc

Bi 2201

END