24 research outputs found
Feynman's Propagator Applied to Network Models of Localization
Network models of dirty electronic systems are mapped onto an interacting
field theory of lower dimensionality by intepreting one space dimension as
time. This is accomplished via Feynman's interpretation of anti-particles as
particles moving backwards in time. The method developed maps calculation of
the moments of the Landauer conductance onto calculation of correlation
functions of an interacting field theory of bosons and fermions. The resulting
field theories are supersymmetric and closely related to the supersymmetric
spin-chain representations of network models recently discussed by various
authors. As an application of the method, the two-edge Chalker-Coddington model
is shown to be Anderson localized, and a delocalization transition in a related
two-edge network model (recently discussed by Balents and Fisher) is studied by
calculation of the average Landauer conductance.Comment: Latex, 14 pages, 2 fig
Transport of Surface States in the Bulk Quantum Hall Effect
The two-dimensional surface of a coupled multilayer integer quantum Hall
system consists of an anisotropic chiral metal. This unusual metal is
characterized by ballistic motion transverse and diffusive motion parallel
(\hat{z}) to the magnetic field. Employing a network model, we calculate
numerically the phase coherent two-terminal z-axis conductance and its
mesoscopic fluctuations. Quasi-1d localization effects are evident in the limit
of many layers. We consider the role of inelastic de-phasing effects in
modifying the transport of the chiral surface sheath, discussing their
importance in the recent experiments of Druist et al.Comment: 9 pages LaTex, 9 postscript figures included using eps
Multifractality at the spin quantum Hall transition
Statistical properties of critical wave functions at the spin quantum Hall
transition are studied both numerically and analytically (via mapping onto the
classical percolation). It is shown that the index characterizing the
decay of wave function correlations is equal to 1/4, at variance with the
decay of the diffusion propagator. The multifractality spectra of
eigenfunctions and of two-point conductances are found to be
close-to-parabolic, and .Comment: 4 pages, 3 figure
Superconducting ``metals'' and ``insulators''
We propose a characterization of zero temperature phases in disordered
superconductors on the basis of the nature of quasiparticle transport. In three
dimensional systems, there are two distinct phases in close analogy to the
distinction between normal metals and insulators: the superconducting "metal"
with delocalized quasiparticle excitations and the superconducting "insulator"
with localized quasiparticles. We describe experimental realizations of either
phase, and study their general properties theoretically. We suggest experiments
where it should be possible to tune from one superconducting phase to the
other, thereby probing a novel "metal-insulator" transition inside a
superconductor. We point out various implications of our results for the phase
transitions where the superconductor is destroyed at zero temperature to form
either a normal metal or a normal insulator.Comment: 18 page
Fokker-Planck equations and density of states in disordered quantum wires
We propose a general scheme to construct scaling equations for the density of
states in disordered quantum wires for all ten pure Cartan symmetry classes.
The anomalous behavior of the density of states near the Fermi level for the
three chiral and four Bogoliubov-de Gennes universality classes is analysed in
detail by means of a mapping to a scaling equation for the reflection from a
quantum wire in the presence of an imaginary potential.Comment: 10 pages, 5 figures, revised versio
Plateaux Transitions in the Pairing Model:Topology and Selection Rule
Based on the two-dimensional lattice fermion model, we discuss transitions
between different pairing states. Each phase is labeled by an integer which is
a topological invariant and characterized by vortices of the Bloch
wavefunction. The transitions between phases with different integers obey a
selection rule. Basic properties of the edge states are revealed. They reflect
the topological character of the bulk. Transitions driven by randomness are
also discussed numerically.Comment: 8 pages with 2 postscript figures, RevTe
Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
When the two-dimensional random-bond Ising model is represented as a
noninteracting fermion problem, it has the same symmetries as an ensemble of
random matrices known as class D. A nonlinear sigma model analysis of the
latter in two dimensions has previously led to the prediction of a metallic
phase, in which the fermion eigenstates at zero energy are extended. In this
paper we argue that such behavior cannot occur in the random-bond Ising model,
by showing that the Ising spin correlations in the metallic phase violate the
bound on such correlations that results from the reality of the Ising
couplings. Some types of disorder in spinless or spin-polarized p-wave
superconductors and paired fractional quantum Hall states allow a mapping onto
an Ising model with real but correlated bonds, and hence a metallic phase is
not possible there either. It is further argued that vortex disorder, which is
generic in the fractional quantum Hall applications, destroys the ordered or
weak-pairing phase, in which nonabelian statistics is obtained in the pure
case.Comment: 13 pages; largely independent of cond-mat/0007254; V. 2: as publishe
Liouvillian Approach to the Integer Quantum Hall Effect Transition
We present a novel approach to the localization-delocalization transition in
the integer quantum Hall effect. The Hamiltonian projected onto the lowest
Landau level can be written in terms of the projected density operators alone.
This and the closed set of commutation relations between the projected
densities leads to simple equations for the time evolution of the density
operators. These equations can be used to map the problem of calculating the
disorder averaged and energetically unconstrained density-density correlation
function to the problem of calculating the one-particle density of states of a
dynamical system with a novel action. At the self-consistent mean-field level,
this approach yields normal diffusion and a finite longitudinal conductivity.
While we have not been able to go beyond the saddle point approximation
analytically, we show numerically that the critical localization exponent can
be extracted from the energetically integrated correlation function yielding
in excellent agreement with previous finite-size scaling
studies.Comment: 9 pages, submitted to PR
Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
We study fluctuations of the local density of states (LDOS) on a tree-like
lattice with large branching number . The average form of the local spectral
function (at given value of the random potential in the observation point)
shows a crossover from the Lorentzian to semicircular form at ,
where , is the typical value of the hopping matrix
element, and is the width of the distribution of random site energies. For
the LDOS fluctuations (with respect to this average form) are
weak. In the opposite case, , the fluctuations get strong and the
average LDOS ceases to be representative, which is related to the existence of
the Anderson transition at . On the localized side
of the transition the spectrum is discrete, and LDOS is given by a set of
-like peaks. The effective number of components in this regime is given
by , with being the inverse participation ratio. It is shown that
has in the transition point a limiting value close to unity, , so that the system undergoes a transition directly from the deeply
localized to extended phase. On the side of delocalized states, the peaks in
LDOS get broadened, with a width being exponentially small near the
transition point. We discuss application of our results to the problem of the
quasiparticle line shape in a finite Fermi system, as suggested recently by
Altshuler, Gefen, Kamenev, and Levitov.Comment: 12 pages, 1 figure. Misprints in eqs.(21) and (28) corrected, section
VII added. Accepted for publication in Phys. Rev.
Unitary limit and quantum interference effect in disordered two-dimensional crystals with nearly half-filled bands
Based on the self-consistent -matrix approximation, the quantum
interference (QI) effect is studied with the diagrammatic technique in
weakly-disordered two-dimensional crystals with nearly half-filled bands. In
addition to the usual 0-mode cooperon and diffuson, there exist -mode
cooperon and diffuson in the unitary limit due to the particle-hole symmetry.
The diffusive -modes are gapped by the deviation from the exactly-nested
Fermi surface. The conductivity diagrams with the gapped -mode cooperon or
diffuson are found to give rise to unconventional features of the QI effect.
Besides the inelastic scattering, the thermal fluctuation is shown to be also
an important dephasing mechanism in the QI processes related with the diffusive
-modes. In the proximity of the nesting case, a power-law
anti-localization effect appears due to the -mode diffuson. For large
deviation from the nested Fermi surface, this anti-localization effect is
suppressed, and the conductivity remains to have the usual logarithmic
weak-localization correction contributed by the 0-mode cooperon. As a result,
the dc conductivity in the unitary limit becomes a non-monotonic function of
the temperature or the sample size, which is quite different from the
prediction of the usual weak-localization theory.Comment: 21 pages, 4 figure