16 research outputs found
The Upper Critical Field in Disordered Two-Dimensional Superconductors
We present calculations of the upper critical field in superconducting films
as a function of increasing disorder (as measured by the normal state
resistance per square). In contradiction to previous work, we find that there
is no anomalous low-temperature positive curvature in the upper critical field
as disorder is increased. We show that the previous prediction of this effect
is due to an unjustified analytical approximation of sums occuring in the
perturbative calculation. Our treatment includes both a careful analysis of
first-order perturbation theory, and a non-perturbative resummation technique.
No anomalous curvature is found in either case. We present our results in
graphical form.Comment: 11 pages, 8 figure
Effect of Magnetic Impurities on Suppression of the Transition Temperature in Disordered Superconductors
We calculate the first-order perturbative correction to the transition
temperature in a superconductor with both non-magnetic and magnetic
impurities. We do this by first evaluating the correction to the effective
potential, , and then obtain the first-order correction to the
order parameter, , by finding the minimum of . Setting
finally allows to be evaluated. is now a function of
both the resistance per square, , a measure of the non-magnetic
disorder, and the spin-flip scattering rate, , a measure of the
magnetic disorder. We find that the effective pair-breaking rate per magnetic
impurity is virtually independent of the resistance per square of the film, in
agreement with an experiment of Chervenak and Valles. This conclusion is
supported by both the perturbative calculation, and by a non-perturbative
re-summation technique.Comment: 29 pages, 9 figure
Phase coherence phenomena in superconducting films
Superconducting films subject to an in-plane magnetic field exhibit a gapless
superconducting phase. We explore the quasi-particle spectral properties of the
gapless phase and comment on the transport properties. Of particular interest
is the sensitivity of the quantum interference phenomena in this phase to the
nature of the impurity scattering. We find that films subject to columnar
defects exhibit a `Berry-Robnik' symmetry which changes the fundamental
properties of the system. Furthermore, we explore the integrity of the gapped
phase. As in the magnetic impurity system, we show that optimal fluctuations of
the random impurity potential conspire with the in-plane magnetic field to
induce a band of localized sub-gap states. Finally, we investigate the
interplay of the proximity effect and gapless superconductivity in thin normal
metal-superconductor bi-layers.Comment: 13 pages, 8 figures include
Mean-field Phase Diagram of Two-Dimensional Electrons with Disorder in a Weak Magnetic Field
We study two-dimensional interacting electrons in a weak perpendicular
magnetic field with the filling factor and in the presence of a
quenched disorder. In the framework of the Hartree-Fock approximation, we
obtain the mean-field phase diagram for the partially filled highest Landau
level. We find that the CDW state can exist if the Landau level broadening
does not exceed the critical value .
Our analysis of weak crystallization corrections to the mean-field results
shows that these corrections are of the order of and
therefore can be neglected
Gap Fluctuations in Inhomogeneous Superconductors
Spatial fluctuations of the effective pairing interaction between electrons
in a superconductor induce variations of the order parameter which in turn lead
to significant changes in the density of states. In addition to an overall
reduction of the quasi-particle energy gap, theory suggests that mesoscopic
fluctuations of the impurity potential induce localised tail states below the
mean-field gap edge. Using a field theoretic approach, we elucidate the nature
of the states in the `sub-gap' region. Specifically, we show that these states
are associated with replica symmetry broken instanton solutions of the
mean-field equations.Comment: 11 pages, 3 figures included. To be published in PRB (Sept. 2001
Electrons in an annealed environment: A special case of the interacting electron problem
The problem of noninteracting electrons in the presence of annealed magnetic
disorder, in addition to nonmagnetic quenched disorder, is considered. It is
shown that the proper physical interpretation of this model is one of electrons
interacting via a potential that is long-ranged in time, and that its technical
analysis by means of renormalization group techniques must also be done in
analogy to the interacting problem. As a result, and contrary to previous
claims, the model does not simply describe a metal-insulator transition in
() dimensions. Rather, it describes a transition
to a ferromagnetic state that, as a function of the disorder, precedes the
metal-insulator transition close to . In , a transition from a
paramagnetic metal to a paramagnetic insulator is possible.Comment: 13 pp., LaTeX, 2 eps figs; final version as publishe
Superconductivity and Charge Density Wave in a Quasi-One-Dimensional Spin Gap System
We consider a model of spin-gapped chains weakly coupled by Josephson and
Coulomb interactions. Combining such non-perturbative methods as bosonization
and Bethe ansatz to treat the intra-chain interactions with the Random Phase
Approximation for the inter-chain couplings and the first corrections to this,
we investigate the phase diagram of this model. The phase diagram shows both
charge density wave ordering and superconductivity. These phases are seperated
by a line of critical points which exhibits an approximate an SU(2) symmetry.
We consider the effects of a magnetic field on the system. We apply the theory
to the material Sr_2 Ca_12 Cu_24 O_41 and suggest further experiments.Comment: 14 pages, 7 figure; submitted to PRB; Revised with new version:
references added; section on the flux state remove
Conductance oscillations in strongly correlated fractional quantum Hall line junctions
We present a detailed theory of transport through line junctions formed by
counterpropagating single-branch fractional-quantum-Hall edge channels having
different filling factors. Intriguing transport properties are exhibited when
strong Coulomb interactions between electrons from the two edges are present.
Such strongly correlated line junctions can be classified according to the
value of an effective line-junction filling factor n that is the inverse of an
even integer. Interactions turn out to affect transport most importantly for
n=1/2 and n=1/4. A particularly interesting case is n=1/4 corresponding to,
e.g., a junction of edge channels having filling factor 1 and 1/5,
respectively. We predict its differential tunneling conductance to oscillate as
a function of voltage. This behavior directly reflects the existence of novel
Majorana-fermion quasiparticle excitations in this type of line junction.
Experimental accessibility of such systems in current cleaved-edge overgrown
samples enables direct testing of our theoretical predictions.Comment: 2 figures, 10 pages, RevTex4, v2: added second figure for clarit
Anomalous Quantum Diffusion at the Superfluid-Insulator Transition
We consider the problem of the superconductor-insulator transition in the
presence of disorder, assuming that the fermionic degrees of freedom can be
ignored so that the problem reduces to one of Cooper pair localization. Weak
disorder drives the critical behavior away from the pure critical point,
initially towards a diffusive fixed point. We consider the effects of Coulomb
interactions and quantum interference at this diffusive fixed point. Coulomb
interactions enhance the conductivity, in contrast to the situation for
fermions, essentially because the exchange interaction is opposite in sign. The
interaction-driven enhancement of the conductivity is larger than the
weak-localization suppression, so the system scales to a perfect conductor.
Thus, it is a consistent possibility for the critical resistivity at the
superconductor-insulator transition to be zero, but this value is only
approached logarithmically. We determine the values of the critical exponents
and comment on possible implications for the interpretation of
experiments
Shot Noise at High Temperatures
We consider the possibility of measuring non-equilibrium properties of the
current correlation functions at high temperatures (and small bias). Through
the example of the third cumulant of the current () we demonstrate
that odd order correlation functions represent non-equilibrium physics even at
small external bias and high temperatures. We calculate for a quasi-one-dimensional diffusive constriction. We calculate the
scaling function in two regimes: when the scattering processes are purely
elastic and when the inelastic electron-electron scattering is strong. In both
cases we find that interpolates between two constants. In the low (high)
temperature limit is strongly (weakly) enhanced (suppressed) by the
electron-electron scattering.Comment: 11 pages 4 fig. submitted to Phys. Rev.