Transcript No Slide Title

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.
2.
3.
4.
5.
Introduction
Vortex Nernst effect
Enhanced Diamagnetism
Fragile London rigidity T>Tc
Low-temp. Quantum Vortex Liquid State
Hong Kong Univ, Dec. 2006
Thanks, Patrick!
1. (1975-80)
Sliding charge density waves (LRA)
Pinning and Depinning, FLR length
BC
AD
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
Phase diagram of cuprates
Mott insulator
s = 1/2
pseudogap
T
T*
vortex liquidTc
AF
0
dSC
0.05
Fermi
liquid
0.25
doping x (fraction of sites with holes)
Spontaneous vorticity destroys superfluidity
hole
Josephson Effect, phase-slip and Nernst signal
Passage of a vortex
Phase diff. f jumps by 2p
Phase difference

2eVJ   f = 2ph nV
2p
Josephson Eq.
f
VJ
Integrate VJ to give dc signal
prop. to nv
t
Nernst effect experiment
Wang et al. PRB 2001
Bi 2212 (UD)
Tc
Vortices move in a temperature gradient
Phase slip generates Josephson voltage
2eVJ = 2ph nV
EJ = B x v
ey = Ey /|
T|
(Nernst signal)
Nernst signal persists high
above Tc
Wang, Li, NPO PRB 2006
Giant Nernst signal in cuprates
overdoped
underdoped
optimal
Nernst signal
eN = Ey /|
T|
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
Free energy gain
DF = U - TS
Mean-field phase diagram
Cuprate phase diagram
2H-NbSe2
4T
100 T
normal
Hc2
liquid
Hm H
H
Hc2
vortex solid
Hm
Hc1
0
T
Meissner state
Tc0
7K
vortex
solid
vortex
liquid
Tc
100 K
Vortex unbinding
in H = 0
Implications of Giant Nernst signal
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?
Diamagnetic currents in vortex liquid
Supercurrents follow contours of condensate
Js = -(eh/m)
x |Y|2 z
Torque magnetometry
Mike Naughton
(Boston College)
=m×B
Torque on moment:
crystal

×
B
f
Deflection of cantilever:
m
 = k f
Underdoped
Bi 2212
Wang et al.
PRL 2005
Tc
Magnetization curves in underdoped Bi 2212
Wang
etal.al.
Wang et
Cond-mat/05
PRL
2005
Tc
Separatrix Ts
At high T, M scales with Nernst signal eN
M
Hc2
Lu Li et al., unpubl.
H
M = - [Hc2 – H] / b(2k2 –1)
UN Bi 2212
“Fragile” London rigidity above Tc
Above Tc, M/H is singular
M ~ -H1/d (c is divergent)
Lu Li et al. Europhys Lett 2005
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
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
The phase diagram
in x-H plane at low T
Nernst
region
H
0
?
0.1
x
0.2
0.3
Magnetization in lightly doped La2-xSrxCuO4
Lu Li et al., unpubl.
Evidence for robust diagmagnetism for x < xc
Doping x
Lu Li et al., unpubl.
Diamagnetism coexists with growing spin population
Vortex solid-to-liquid transition for x < xc
Debye Waller dependence
Lu Li et al., unpubl.
Hm(T) = H0 exp(-T/T0)
Low temp Phase Diagram
H
0
0.1
x
0.2
0.3
Critical Point
Lu Li et al., unpubl.
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 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