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Introduction Vortex Nernst effect Enhanced Diamagnetism Fragile London rigidity T>Tc

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Vorticity and the Phase Diagram of Cuprates

Lu Li,J. G. Checkelsky, N.P.O. Princeton Univ.

Yayu Wang, PrincetonU.,U.C. Berkeley

M. J. Naughton, Boston College

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

S. Uchida, Univ. Tokyo

Genda Gu, Brookhaven National Lab

- Introduction
- Vortex Nernst effect
- Enhanced Diamagnetism
- Fragile London rigidity T>Tc
- Low-temp. Quantum Vortex Liquid State

Hong Kong Univ, Dec. 2006

BC

AD

Thanks, Patrick!

- 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 quasiparticles
- Thermal Hall effect and qp-vortex scattering
- 5. (2000 -- )
- Strong fluctuations in pseudogap state

vortex liquid

AF

dSC

Phase diagram of cuprates

Mott insulator

s = 1/2

hole

T*

pseudogap

T

Tc

Fermi

liquid

0

0.25

0.05

doping x

(fraction of sites with holes)

Spontaneous vorticity destroys superfluidity

= 2ph nV

2p

f

Integrate VJ to give dc signal

prop. to nv

VJ

t

Josephson Effect, phase-slip and Nernst signal

Passage of a vortex

Phase diff. f jumps by 2p

Josephson Eq.

Phase difference

Vortices move in a temperature gradient

Phase slip generates Josephson voltage

2eVJ = 2ph nV

EJ = B x v

ey = Ey /| T |

Wang et al. PRB 2001

Nernst effect experiment

Bi 2212 (UD)

Tc

Nernst signal persists high

above Tc

(Nernst signal)

Giant Nernst signal in cuprates

Wang, Li, NPO PRB 2006

Nernst signal

eN = Ey /| T |

underdoped

optimal

overdoped

Vortex-Nernst signal in Bi 2201

Wang, Li, Ong PRB 2006

Nernst

region

- Condensate amplitude persists to Tonset > Tc
- Nernst signal confined to SC dome
- Vorticity defines Nernst region

Kosterlitz Thouless transition in 2D superconductor

vortex density

antivortex

vortex

Unbinding of

vortex-antivortex

DF = U - TS

Free energy gain

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

Vortex unbinding

in H = 0

100 K

7 K

Meissner state

Implications of Giant Nernst signal

- Vorticity persists high above Tc
- Confined to SC “dome”
- 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?

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

Diamagnetic currents in vortex liquid

Supercurrents follow contours of condensate

×

B

m

Torque magnetometry

Mike Naughton

(Boston College)

Torque on moment: = m × B

crystal

Deflection of cantilever: = k

Underdoped

Bi 2212

Wang et al.

PRL 2005

Tc

Magnetization curves in underdoped Bi 2212

Wang et al.

PRL 2005

Wang et al.

Cond-mat/05

Tc

Separatrix Ts

At high T, M scales with Nernst signal eN

Hc2

M

H

M = - [Hc2 – H] / b(2k2 –1)

Lu Li et al., unpubl.

UN Bi 2212

“Fragile” London rigidity above Tc

Lu Li et al. Europhys Lett 2005

Above Tc, M/H is singular

M ~ -H1/d (c is divergent)

Non-analytic magnetization above Tc

M ~ H1/d

Fractional-exponent

region

- In hole-doped cuprates
- 1. Large region in phase diagram above Tc dome
- with enhanced Nernst signal
- Associated with vortex excitations (not Gaussian)
- Confirmed by torque magnetometry
- Transition at Tc is 3D version of KT transition
- (loss of phase coherence)
- 5. Upper critical field behavior confirms conclusion

H

?

0.3

0.2

0

0.1

x

The phase diagram

in x-H plane at low T

Nernst

region

Magnetization in lightly doped La2-xSrxCuO4

Lu Li et al., unpubl.

Evidence for robust diagmagnetism for x < xc

Lu Li et al., unpubl.

Doping x

Diamagnetism coexists with growing spin population

Vortex solid-to-liquid transition for x < xc

Lu Li et al., unpubl.

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

H

0.3

0.2

0

0.1

x

Lu Li et al., unpubl.

Low temp Phase Diagram

Critical Point

- Low-temperature vortex liquid
- Vortex solid surrounded by vortex liquid at 0.35 K
- Sharp quantum transition at xc = 0.055. Quantum vortices destroy phase coherence
- At 0.35 K, pair condensate survives without phase rigidity even for x = 0.03
- Melting of vortex solid appears to be classical at 0.35 K (Debye-Waller like).

- Summary
- Nernst region is suffused with vorticity,
- enhanced diamagnetism and
- finite pairing amplitude
- Extends from Tc to Tonset < T*
- Nernst region dominates lower temp part of
- Pseudogap state
- 4.Depairing field Hc2 and binding energy are
- very large
- Strong pairing potential but soft phase rigidity
- 5.Vortex-liquid state is ground state below xc

Bi 2201

END