321 research outputs found
Conductance distributions in disordered quantum spin-Hall systems
We study numerically the charge conductance distributions of disordered
quantum spin-Hall (QSH) systems using a quantum network model. We have found
that the conductance distribution at the metal-QSH insulator transition is
clearly different from that at the metal-ordinary insulator transition. Thus
the critical conductance distribution is sensitive not only to the boundary
condition but also to the presence of edge states in the adjacent insulating
phase. We have also calculated the point-contact conductance. Even when the
two-terminal conductance is approximately quantized, we find large fluctuations
in the point-contact conductance. Furthermore, we have found a semi-circular
relation between the average of the point-contact conductance and its
fluctuation.Comment: 9 pages, 17 figures, published versio
Transmission eigenvalues and the bare conductance in the crossover to Anderson localization
We measure the field transmission matrix t for microwave radiation
propagating through random waveguides in the crossover to Anderson
localization. From these measurements, we determine the dimensionless
conductance, g, and the individual eigenvalues of the transmission
matrix whose sum equals g. In diffusive samples, the highest
eigenvalue, , is close to unity corresponding to a transmission of
nearly 100%, while for localized waves, the average of , is nearly
equal to g. We find that the spacing between average values of is
constant and demonstrate that when surface interactions are taken into account
it is equal to the inverse of the bare conductance.Comment: 5 pages, 5 figure
Anderson localization from the replica formalism
We study Anderson localization in quasi--one--dimensional disordered wires
within the framework of the replica --model. Applying a semiclassical
approach (geodesic action plus Gaussian fluctuations) recently introduced
within the context of supersymmetry by Lamacraft, Simons and Zirnbauer
\cite{LSZ}, we compute the {\em exact} density of transmission matrix
eigenvalues of superconducting wires (of symmetry class I.) For the unitary
class of metallic systems (class ) we are able to obtain the density
function, save for its large transmission tail.Comment: 4 pages, 1 figur
Flux Dependence of Persistent Current in a Mesoscopic Disordered Tight Binding Ring
We reconsider the study of persistent currents in a disordered
one-dimensional ring threaded by a magnetic flux, using he one-band
tight-binding model for a ring of N-sites with random site energies. The
secular equation for the eigenenergies expressed in terms of transfer matrices
in the site representation is solved exactly to second order in a perturbation
theory for weak disorder and fluxes differing from half-integer multiples of
the elementary flux quantum. From the equilibrium currents associated with the
one-electron eigenstates we derive closed analytic expressions for the disorder
averaged persistent current for even and odd numbers, Ne, of electrons in the
ground state. Explicit discussion for the half-filled band case confirms that
the persistent current is flux periodic as in the absence of disorder, and that
its amplitude is generally suppressed by the effect of the disorder. In
comparison to previous results, based on an approximate analysis of the secular
equation, the current suppression by disorder is strongly enhanced by a new
flux-dependent factor.Comment: 15 pages, LaTex 2
Inhomogeneous Fixed Point Ensembles Revisited
The density of states of disordered systems in the Wigner-Dyson classes
approaches some finite non-zero value at the mobility edge, whereas the density
of states in systems of the chiral and Bogolubov-de Gennes classes shows a
divergent or vanishing behavior in the band centre. Such types of behavior were
classified as homogeneous and inhomogeneous fixed point ensembles within a
real-space renormalization group approach. For the latter ensembles the scaling
law was derived for the power laws of the density of states
and of the localization length .
This prediction from 1976 is checked against explicit results obtained
meanwhile.Comment: Submitted to 'World Scientific' for the volume 'Fifty Years of
Anderson Localization'. 12 page
Localization in disordered superconducting wires with broken spin-rotation symmetry
Localization and delocalization of non-interacting quasiparticle states in a
superconducting wire are reconsidered, for the cases in which spin-rotation
symmetry is absent, and time-reversal symmetry is either broken or unbroken;
these are referred to as symmetry classes BD and DIII, respectively. We show
that, if a continuum limit is taken to obtain a Fokker-Planck (FP) equation for
the transfer matrix, as in some previous work, then when there are more than
two scattering channels, all terms that break a certain symmetry are lost. It
was already known that the resulting FP equation exhibits critical behavior.
The additional symmetry is not required by the definition of the symmetry
classes; terms that break it arise from non-Gaussian probability distributions,
and may be kept in a generalized FP equation. We show that they lead to
localization in a long wire. When the wire has more than two scattering
channels, these terms are irrelevant at the short distance (diffusive or
ballistic) fixed point, but as they are relevant at the long-distance critical
fixed point, they are termed dangerously irrelevant. We confirm the results in
a supersymmetry approach for class BD, where the additional terms correspond to
jumps between the two components of the sigma model target space. We consider
the effect of random fluxes, which prevent the system localizing. We show
that in one dimension the transitions in these two symmetry classes, and also
those in the three chiral symmetry classes, all lie in the same universality
class
Higher-order mesoscopic fluctuations in quantum wires: Conductance and current cumulants
We study conductance cumulants and current cumulants
related to heat and electrical transport in coherent mesoscopic quantum wires
near the diffusive regime. We consider the asymptotic behavior in the limit
where the number of channels and the length of the wire in the units of the
mean free path are large but the bare conductance is fixed. A recursion
equation unifying the descriptions of the standard and Bogoliubov--de Gennes
(BdG) symmetry classes is presented. We give values and come up with a novel
scaling form for the higher-order conductance cumulants. In the BdG wires, in
the presence of time-reversal symmetry, for the cumulants higher than the
second it is found that there may be only contributions which depend
nonanalytically on the wire length. This indicates that diagrammatic or
semiclassical pictures do not adequately describe higher-order spectral
correlations. Moreover, we obtain the weak-localization corrections to
with .Comment: 7 page
Nonchiral Edge States at the Chiral Metal Insulator Transition in Disordered Quantum Hall Wires
The quantum phase diagram of disordered wires in a strong magnetic field is
studied as a function of wire width and energy. The two-terminal conductance
shows zero-temperature discontinuous transitions between exactly integer
plateau values and zero. In the vicinity of this transition, the chiral
metal-insulator transition (CMIT), states are identified that are
superpositions of edge states with opposite chirality. The bulk contribution of
such states is found to decrease with increasing wire width. Based on exact
diagonalization results for the eigenstates and their participation ratios, we
conclude that these states are characteristic for the CMIT, have the appearance
of nonchiral edges states, and are thereby distinguishable from other states in
the quantum Hall wire, namely, extended edge states, two-dimensionally (2D)
localized, quasi-1D localized, and 2D critical states.Comment: replaced with revised versio
Ballistic transport in disordered graphene
An analytic theory of electron transport in disordered graphene in a
ballistic geometry is developed. We consider a sample of a large width W and
analyze the evolution of the conductance, the shot noise, and the full
statistics of the charge transfer with increasing length L, both at the Dirac
point and at a finite gate voltage. The transfer matrix approach combined with
the disorder perturbation theory and the renormalization group is used. We also
discuss the crossover to the diffusive regime and construct a ``phase diagram''
of various transport regimes in graphene.Comment: 23 pages, 10 figure
Quantum Transparency of Anderson Insulator Junctions: Statistics of Transmission Eigenvalues, Shot Noise, and Proximity Conductance
We investigate quantum transport through strongly disordered barriers, made
of a material with exceptionally high resistivity that behaves as an Anderson
insulator or a ``bad metal'' in the bulk, by analyzing the distribution of
Landauer transmission eigenvalues for a junction where such barrier is attached
to two clean metallic leads. We find that scaling of the transmission
eigenvalue distribution with the junction thickness (starting from the single
interface limit) always predicts a non-zero probability to find high
transmission channels even in relatively thick barriers. Using this
distribution, we compute the zero frequency shot noise power (as well as its
sample-to-sample fluctuations) and demonstrate how it provides a single number
characterization of non-trivial transmission properties of different types of
disordered barriers. The appearance of open conducting channels, whose
transmission eigenvalue is close to one, and corresponding violent mesoscopic
fluctuations of transport quantities explain at least some of the peculiar
zero-bias anomalies in the Anderson-insulator/superconductor junctions observed
in recent experiments [Phys. Rev. B {\bf 61}, 13037 (2000)]. Our findings are
also relevant for the understanding of the role of defects that can undermine
quality of thin tunnel barriers made of conventional band-insulators.Comment: 9 pages, 8 color EPS figures; one additional figure on mesoscopic
fluctuations of Fano facto
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