The NERNST EFFECT IS NOT BLACK HOLE PHYSICS

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The NERNST EFFECT IS NOT BLACK HOLE PHYSICS
Wang, Li, Ong, pwa We have learned a lot about
cuprates from it
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OUTLINE
1 Vortex Fluid a distinct state of
matter. defined by ?s?0, ??2?0 2 Does not
screen field vortices 3Dynamics supercurrents
relax with ?--viscosity for vortices. 4 The
Nernst Effect e determined by viscosity, energy
of vortex currents. 5 Magnitude of N E
viscosity 6 B, T dependence d-wave gap. 7
deducing gap distribution
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Nernst experiment
ey
Hm
H
Philip Anderson energy of int wiith field B?M/2
so M ?to e
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phase diagram
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Why vortex fluid in cuprates?
Spin-charge locking RVB Gap is
electrons charge triad locks
so that ? becomes a self-energy, leaving ? as a
d-wave gap, which remains constant through Tc,
which is a phase dis- ordering as experimentally
observed. (Locking energy gtgtTc) We assume a
finite ?s and supercurrent
which fluctuates in space and time, having a time
correlation function
We assume the pair current is conserved.
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theory of vortex liquid
Superflows at any time described by a
fluctuating tangle of vortices with curl and div
J0, uniquely so. In the following I use the
Kosterlitz-Thouless 2D model as exemplar but the
key point generalizes to 3D
The energy is (aside from cores) all flow energy
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theory of vortex liquid cont.
evaluating this using a lower cutoff a for size
of vortex cores, and an upper cutoff at the
sample size, gives simply
This is not the expression used by K-T. They
omitted the first term assuming no net vorticity
(or ignoring vortex self-energy). This one
depends on sample size or, if sample in a
B-field, on RlB, the distance between
field vortices. (Feynman)
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Nernst magnitude calculation
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TTc
e
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data from wangOD
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Nernst Effect Magic Formula
formula for ?xy due to vortices
note that this measures the curvature of ? vs B
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Deducing the gap distribution
The gap distibution is unknown except crudely so
lets deduce it from the magic formula instead of
guessing. By calculating ey/B-dey/dB as a
function of B we get a number proportional to
This had better monotonically decrease with T and
with B! Some typical data from Y Wang thesis
(need low Tc to get Hc2 range, method works best
for 2D underdoped)
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LSCO-0.07 Tc 11K
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Bi2201 (La-0.7) Tc 12K
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Bi2201 (La-0.2) Tc 22K
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Bi2201 (La-0.4) Tc 28K
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remarks and conclusion
fits are very inaccurate and plagued by
measurement and even systematic errors. 1 at
low B and T nr Tc, crit fluctuation 2 even worse
for M 3 inhomogeneity 4 but I think data support
vortex fluid strongly, especially BlnB idea
incompressible vortex fluid 5 They also support,
roughly, Fermi arc idea the small gaps disappear
first.
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conclusions
Vortex Liquid theory gives adequate, if not
precise, account of conductivity--Timusk and
Homes observations (therefore qualitative acct of
Tc) Nernst Effect magnitude and shape
Questions and to be done Is Ong-Orenstein a
separate phase? I think so M(B) note
nonlinearity, tracks e(B). What lies above?