151 research outputs found
Low energy theory of disordered graphene
At low values of external doping graphene displays a wealth of unconventional
transport properties. Perhaps most strikingly, it supports a robust 'metallic'
regime, with universal conductance of the order of the conductance quantum. We
here apply a combination of mean field and bosonization methods to explore the
large scale transport properties of the system. We find that, irrespective of
the doping level, disordered graphene is subject to common mechanisms of
Anderson localization. However, at low doping a number of renormalization
mechanisms conspire to protect the conductivity of the system, to an extend
that strong localization may not be seen even at temperatures much smaller than
those underlying present experimental work.Comment: 4 page
Quasi-Particle density of states and Thouless conductance of disordered d-wave superconductors
We present a numerical study of the quasi-particle density of states (DoS) of
two-dimensional d-wave superconductors in the presence of disorder, focusing on
the influence of the range of the disorder. We find qualitatively different
behavior for smooth and short-ranged disorder. In the former case, we find
power law scaling of the DoS with an exponent depending on the strength of the
disorder and the superconducting order parameter in quantitative agreement with
the theory of Nersesyan {\em et al.}. For strong disorder, a qualitative change
to an energy independent DoS occurs.
In contrast, for short-ranged disorder of sufficient strength, we find
localization by analyzing the system size dependence of the Thouless numbers.
Near zero energy we find a micro gap in the DoS. The width of this micro gap is
given by the mean level spacing of a localization volume. From the system size
and disorder dependence of the width of the micro gap we derive the dependence
of the localization length on the disorder strength.Comment: 2 pages, to appear in J. Phys. Soc. Jpn., proceedings Localisation
2002 (Tokyo, Japan
Class D spectral peak in Majorana quantum wires
Proximity coupled spin-orbit quantum wires have recently been shown to
support midgap Majorana states at critical points. We show that in the presence
of disorder these systems are prone to the buildup of a second bandcenter
anomaly, which is of different physical origin but shares key characteristics
with the Majorana state: it is narrow in width, insensitive to magnetic fields,
carries unit spectral weight, and is rigidly tied to the band center. Depending
on the parity of the number of subgap quasiparticle states, a Majorana mode
does or does not coexist with the impurity generated peak. The strong
'entanglement' between the two phenomena may hinder an unambiguous detection of
the Majorana by spectroscopic techniques.Comment: 4+ pages, 3 figures, qualitative discussion is adde
Effective field theory of the disordered Weyl semimetal
In disordered Weyl semimetals, mechanisms of topological origin lead to the
protection against Anderson localization, and at the same time to different
types of transverse electromagnetic response -- the anomalous Hall, and chiral
magnetic effect. We here apply field theory methods to discuss the
manifestation of these phenomena at length scales which are beyond the scope of
diagrammatic perturbation theory. Specifically we show how an interplay of
symmetry breaking and the chiral anomaly leads to a field theory containing two
types of topological terms. Generating the unconventional response coefficients
of the system, these terms remain largely unaffected by disorder, i.e.
information on the chirality of the system remains visible even at large length
scales.Comment: 4 pages, 1 figur
Theory of the strongly disordered Weyl semimetal
In disordered Weyl semimetals, mechanisms of topological origin lead to novel
mechanisms of transport, which manifest themselves in unconventional types of
electromagnetic response. Prominent examples of transport phenomena particular
to the Weyl context include the anomalous Hall effect, the chiral magnetic
effect, and the formation of totally field dominated regimes of transport in
which the longitudinal conductance is proportional to an external magnetic
field. In this paper, we discuss the manifestations of these phenomena at large
length scales including the cases of strong disorder and/or magnetic field
which are beyond the scope of diagrammatic perturbation theory. Our perhaps
most striking finding is the identification of a novel regime of
drift/diffusion transport where diffusion at short scales gives way to
effectively ballistic dynamics at large scales, before a re-entrance to
diffusion takes place at yet larger scales. We will show that this regime plays
a key role in understanding the interplay of the various types of
magnetoresponse of the system. Our results are obtained by describing the
strongly disordered system in terms of an effective field theory of
Chern-Simons type. The paper contains a self-contained derivation of this
theory, and a discussion of both equilibrium and non-equilibrium (noise)
transport phenomena following from it.Comment: 26 pages, 7 figure
Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics
We show that the proper inclusion of soft reparameterization modes in the
Sachdev-Ye-Kitaev model of randomly interacting Majorana fermions reduces
its long-time behavior to that of Liouville quantum mechanics. As a result, all
zero temperature correlation functions decay with the universal exponent
for times larger than the inverse single particle level
spacing . In the particular case of the single particle Green
function this behavior is manifestation of the zero-bias anomaly, or scaling in
energy as . We also present exact diagonalization study
supporting our conclusions.Comment: 14 pages, 2 figure
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