Vortex Nernst effect

1
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 College S. Ono, S. Komiya, Yoichi Ando,
CRI, Elec. Power Inst., Tokyo S. Uchida, Univ.
Tokyo Genda Gu, Brookhaven National Lab

1. Introduction
2. Vortex Nernst effect
3. Enhanced Diamagnetism
4. Fragile London rigidity TgtTc
5. Low-temp. Quantum Vortex Liquid State

Hong Kong Univ, Dec. 2006
2
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

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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
4
Josephson Effect, phase-slip and Nernst signal
Passage of a vortex Phase diff. f jumps by 2p

Josephson Eq.
Phase difference
5
Wang et al. PRB 2001
Nernst effect experiment
Bi 2212 (UD)
Tc
Nernst signal persists high above Tc
(Nernst signal)
6
Giant Nernst signal in cuprates
Wang, Li, NPO PRB 2006
underdoped
optimal
overdoped
7
Vortex-Nernst signal in Bi 2201
Wang, Li, Ong PRB 2006
8
Nernst region

• Condensate amplitude persists to Tonset gt Tc
• Nernst signal confined to SC dome
• Vorticity defines Nernst region

9
Kosterlitz Thouless transition in 2D
superconductor
vortex density
antivortex
vortex
Unbinding of vortex-antivortex
DF U - TS
Free energy gain
10
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
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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?
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Diamagnetic currents in vortex liquid
Supercurrents follow contours of condensate
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Torque magnetometry
Mike Naughton (Boston College)
Torque on moment ? m B
crystal
Deflection of cantilever ? k ?
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Underdoped Bi 2212
Wang et al. PRL 2005
Tc
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Magnetization curves in underdoped Bi 2212
Wang et al. PRL 2005
Wang et al. Cond-mat/05
Tc
Separatrix Ts
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At high T, M scales with Nernst signal eN
17
Lu Li et al., unpubl.
UN Bi 2212
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Fragile London rigidity above Tc
Lu Li et al. Europhys Lett 2005
Above Tc, M/H is singular M -H1/d (c is
divergent)
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Non-analytic magnetization above Tc
M H1/d
Fractional-exponent region
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• 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

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The phase diagram in x-H plane at low T
Nernst region
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Magnetization in lightly doped La2-xSrxCuO4
Lu Li et al., unpubl.
Evidence for robust diagmagnetism for x lt xc
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Lu Li et al., unpubl.
Doping x
Diamagnetism coexists with growing spin population
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Vortex solid-to-liquid transition for x lt xc
Lu Li et al., unpubl.
Debye Waller dependence Hm(T) H0 exp(-T/T0)
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Lu Li et al., unpubl.
Low temp Phase Diagram
Critical Point
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• 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).

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• Summary
• Nernst region is suffused with vorticity,
• enhanced diamagnetism and
• finite pairing amplitude
• Extends from Tc to Tonset lt 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
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END