Mixed-state quasiparticle transport in high-T_c cuprates
Discovery by Krishana, Ong and co-workers [Science 277, 83 (1997)] of
the
mysterious high-field plateau in the longitudinal thermal conductivity
$\kappa_{xx}(H)$ of Bi2212 superconductor set theorists scrambling for
possible explanations of this phenomenon.
Such a plateau behavior stands in a stark contrast to the strong
field-dependences
in \kappa_{xx}(H) found in conventional superconductors over the entire
range of fields. More significantly, it has long been recognized that
measurements
of thermal conductivity contain considerable information pertinent to
the
pairing mechanism in cuprates (such as the inelastic scattering rates),
which can however only be extracted if a detailed understanding of the
quasiparticle dynamics in magnetic field is established. The initial
interpretation
of the plateau involved a field-induced transition to a fully gapped
state,
such as the d+id' state proposed by Laughlin, which would effectively
freeze
out the quasiparticle transport at low energies. However,
experimentally
there appears to be little additional evidence for such a transition,
except
perhaps for the apparent bound states found by scanning tunneling
microscopy
(STM) in the vortex cores of YBCO which should not exist in a pure
d-wave
state (see below).
I have developed a theory which accounts for the plateau effect in a
very natural way, invoking only the fundamental properties of Dirac
fermions
which are the relevant low-energy excitations in a d-wave
superconductor.
In particular I have demonstrated that, if the vortex array is
disordered,
a field-independent longitudinal thermal conductivity arises quite
naturally
in a pure d-wave state above a crossover field H*. This occurs as a
result
of exact compensation between the enhancement of the quasiparticle
density
of states due to vortices (the ``Volovik effect'') and the reduction in
the quasiparticle mean free path by scattering from vortices. The
limiting
high-field value of \kappa_{xx}(H) is universal just like the impurity
induced universal microwave conductivity predicted by Patrick Lee. The
approach to this limiting value depends on the distribution of vortices
in the sample and will therefore be material and sample dependent, in
agreement
with experimental data. At present I am generalizing this theory to
include
Hall thermal conductivity \kappa_{xy}(H) which is also a measurable
quantity
and is of even greater potential interest since it is strictly
electronic
with no phonon contribution.
[For more details see
Phys.
Rev. Lett. 82, 1760 (1999). ]
Electronic structure of d-wave vortices
Although the notion of unconventional d-wave superconductivity in
high-T_c
cuprate superconductors has been generally accepted for a relatively
long
period of time, the modeling of the vortex dynamics and transport in
the
mixed state of these materials has been based almost exclusively on
conventional
s-wave concepts. This is largely because until very recently the
understanding
of various aspects of the structure of individual vortices in a d-wave
superconductor was either
incomplete or lacking altogether. In collaboration with Z. Tesanovic
(Johns
Hopkins) I have performed the first detailed analysis of this problem
focusing
primarily on the properties of the order parameter and of the
electronic
states near the core. Using a combination of numerical and analytical
techniques
we came to a surprising conclusion that, in a pure $d_{x^2-y^2}$
superconductor,
the vortex core states are delocalized with wave functions extended
along
the gap node directions (see figure), and exhibit continuous energy
spectrum.
This finding is in a sharp contrast to the well known result of Caroli,
de Gennes and Matricon, who showed (more than 30 years ago) that vortex
core in an s-wave superconductor contains a discrete set of
quasiparticle
states, localized on the length scale set by the superconducting
coherence
length. I am presently exploring the consequences of these findings and
investigating in detail the relation of our results to the experimental
data recently obtained using the cutting edge technique of scanning
tunneling
spectroscopy.
[For more details see Phys.
Rev. Lett. 80, 4763 (1998) and Phys.
Rev. Lett. 79, 4513 (1997).]
Spectral properties of underdoped high-T_c cuprates
A large amount of data exists on underdoped cuprates showing a
``pseudogap''
behavior above the superconducting transition temperature T_c which
persists
up to a much higher temperature T^*. One school of thought, put forward
by Emery and Kivelson, explains this behavior by postulating a state
above
T_c with a finite magnitude of a local superconducting order parameter
which, however, has lost its global phase coherence due to
fluctuations.
T^* is then interpreted as the temperature at which the amplitude
vanishes
and the pseudogap is lost. Within such a picture the transition to a
superconducting
state is of a 3D XY type and the physics above T_c is dominated by
fluctuating
unbound vortex-antivortex pairs. A detailed understanding of such a
phase
is lacking at present. With A. J. Millis (Johns Hopkins) we are
currently
performing the very first in-depth analysis of the effect of such a
fluctuating
medium on various physical properties in the psudogap regime. We find
that
photoemission and tunneling spectroscopy data are well accounted for by
a simple model in which mean field d-wave quasiparticles are
semiclasically
coupled to supercurrents induced by fluctuating unbound
vortex-antivortex
pairs. We also conclude that while transverse phase fluctuations are
important
at temperatures above T_c, longitudinal fluctuations are suppressed at
all temperatures. This is in contrast to some theories which suggest
that
longitudinal fluctuations are responsible for the experimentally
observed
suppression of the superfluid density at low temperatures. More
recently
I became interested in dynamical and transport properties of this
pseudogap
regime and I am presently investigating the consequences of the above
scenario
for these quantities.
[For more details see Phys.
Rev. B 58, 14572 (1998) ]
Flux lattices in unconventional superconductors
In collaboration with C. Kallin, A. J. Berlinsky, P. I. Soininen
(McMaster)
and A. L. Fetter (Stanford) we solved the problem of the vortex state
in
a d-wave superconductor in the limiting cases of an isolated vortex
(near
H_{c1}) and of the Abrikosov lattice (near H_{c2}). In view of the fact
that in high-T_c cuprates H_{c2} typically exceeds 100T, most
experiments
are done in the regime of intermediate field H such that H_{c1}<<
H << H_{c2}. Here, strictly speaking, our results do not apply.
In
collaboration with I. Affleck and M. H. S. Amin (UBC) I have formulated
a generalized London model for a d-wave superconductor, which is valid
precisely in this experimentally important regime. For a vortex lattice
this model reproduces very well results obtained from the
Ginzburg-Landau
(G-L) theory, however the physics becomes much more transparent and the
calculations are considerably easier. More recently we have extended
this
model to low temperatures, where the G-L theory does not apply. In this
regime the microscopic effects of d-wave pairing become important and
lead
to a non-local relationship between supercurrent and superfluid
velocity
which becomes singular at T=0. We have shown that this singular
behavior
has profound implications for the structure of the vortex lattice
which,
as a function of decreasing temperature, undergoes a series of sharp
structural
transitions and attains a universal limit at T=0. Such behavior should
be readily observable in experiment and several groups now actively
search
for these effects in the cuprates. [For more
details
see Phys.
Rev. B 58, 5848 (1998),
Phys.
Rev. Lett. 79, 1555 (1997), and Phys.
Rev. B 55, R704 (1997). ]
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