410 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
Crossover of magnetoconductance autocorrelation for a ballistic chaotic quantum dot
The autocorrelation function C_{\varphi,\eps}(\Delta\varphi,\,\Delta \eps)=
\langle \delta g(\varphi,\,\eps)\, \delta
g(\varphi+\Delta\varphi,\,\eps+\Delta \eps)\rangle ( and \eps are
rescaled magnetic flux and energy) for the magnetoconductance of a ballistic
chaotic quantum dot is calculated in the framework of the supersymmetric
non-linear -model. The Hamiltonian of the quantum dot is modelled by a
Gaussian random matrix. The particular form of the symmetry breaking matrix is
found to be relevant for the autocorrelation function but not for the average
conductance. Our results are valid for the complete crossover from orthogonal
to unitary symmetry and their relation with semiclassical theory and an
-matrix Brownian motion ensemble is discussed.Comment: 7 pages, no figures, accepted for publication in Europhysics Letter
Quantum phase transitions in the quasi-periodic kicked rotor
We present a microscopic theory of transport in quasi-periodically driven
environments (`kicked rotors'), as realized in recent atom optic experiments.
We find that the behavior of these systems depends sensitively on the value of
Planck's constant : for irrational values of they
fall into the universality class of disordered electronic systems and we derive
the microscopic theory of the ensuing localization phenomena. In contrast, for
rational values the rotor-Anderson insulator acquires an infinite (static)
conductivity and turns into a `super-metal'. Signatures of the corresponding
metal/super-metal transition are discussed.Comment: 4 pages, 1 figure, 1 tabl
Universal spectral statistics in quantum graphs
We prove that the spectrum of an individual chaotic quantum graph shows
universal spectral correlations, as predicted by random--matrix theory. The
stability of these correlations with regard to non--universal corrections is
analyzed in terms of the linear operator governing the classical dynamics on
the graph.Comment: 4 pages, reftex, 1 figure, revised version to be published in PR
Majorana Fermions in Strongly Interacting Helical Liquids
Majorana fermions were proposed to occur at edges and interfaces of gapped
one-dimensional systems where phases with different topological character meet
due to an interplay of spin-orbit coupling, proximity-induced superconductivity
and external magnetic fields. Here we investigate the effect of strong particle
interactions, and show that the helical liquid offers a mechanism that protects
the very existence of Majorana edge states: whereas moderate interactions close
the proximity gap which supports the edge states, in helical liquids the gap
re-opens due to two-particle processes. However, gapless fermionic excitations
occur at spatial proximity to the Majorana states at interfaces and may
jeopardize their long term Majorana coherence.Comment: 7 pages, 4 figure
Parametric Level Correlations in Random-Matrix Models
We show that parametric level correlations in random-matrix theories are
closely related to a breaking of the symmetry between the advanced and the
retarded Green's functions. The form of the parametric level correlation
function is the same as for the disordered case considered earlier by Simons
and Altshuler and is given by the graded trace of the commutator of the
saddle--point solution with the particular matrix that describes the symmetry
breaking in the actual case of interest. The strength factor differs from the
case of disorder. It is determined solely by the Goldstone mode. It is
essentially given by the number of levels that are strongly mixed as the
external parameter changes. The factor can easily be estimated in applications.Comment: 8 page
Phonons in Random Elastic Media and the Boson Peak
We show that the density of states of random wave equations, normalized by
the square of the frequency, has a peak - sometimes narrow and sometimes broad
- in the range of wave vectors between the disorder correlation length and the
interatomic spacing. The results of this letter may be relevant for
understanding vibrational spectra and light propagation in disordered solids
Enhancement of Persistent Current in Metal Rings by Correlated Disorder
We study analytically the effect of a correlated random potential on the
persistent current in a one-dimensional ring threaded by a magnetic flux
, using an Anderson tight-binding model. In our model, the system of
atomic sites of the ring is assumed to be partitioned into pairs of
identical nearest-neighbour sites (dimers). The site energies for different
dimers are taken to be uncorrelated gaussian variables. For this system we
obtain the exact flux-dependent energy levels to second order in the random
site energies, using an earlier exact transfer matrix perturbation theory.
These results are used to study the mean persistent current generated by
spinless electrons occupying the lowest levels of the
flux-dependent energy band at zero temperature. Detailed analyses are carried
out in the limit and for a half-filled band (), for
magnetic fluxes . While the uncorrelated disorder leads
to a reduction of the persistent current, the disorder correlation acts to
enhance it. In particular, in the half-filled band case the correlated disorder
leads to a global flux-dependent enhancement of persistent current which has
the same form for even and odd . At low filling of the energy band the
effect of the disorder on the persistent current is found to depend on the
parity of : the correlated disorder yields a reduction of the current for
odd and an enhancement of the current for even .Comment: 1
Roadmap to Majorana surface codes
Surface codes offer a very promising avenue towards fault-tolerant quantum
computation. We argue that two-dimensional interacting networks of Majorana
bound states in topological superconductor/semiconductor heterostructures hold
several distinct advantages in that direction, both concerning the hardware
realization and the actual operation of the code. We here discuss how
topologically protected logical qubits in this Majorana surface code
architecture can be defined, initialized, manipulated, and read out. All
physical ingredients needed to implement these operations are routinely used in
topologically trivial quantum devices. In particular, we show that by means of
quantum interference terms in linear conductance measurements, composite
single-electron pumping protocols, and gate-tunable tunnel barriers, the full
set of quantum gates required for universal quantum computation can be
implemented.Comment: 23 pages, 8 figure
Reply to the Comment of den Hartog and van Wees on "Conductance Fluctuations in Mesoscopic Normal-Metal/Superconductor Samples"
In their comment cond-mat/9710285 [Phys. Rev. Lett. 80, 5024 (1998)] den
Hartog and van Wees (HW) raise objections against our analysis of the
experimental data presented in cond-mat/9708162 [Phys. Rev. Lett. 79, 1547
(1997)]. According to HW, we did not account for the quantum phase incoherence
introduced by the Niobium compounds of the investigated Nb/Au hybrid samples.
Here we show that and why this criticism is not justified. Some difficulties
associated with a precise determination of the coherence lengths are discussed.
It is discussed why these uncertainties do not have a qualitative impact on the
results reported in our paper.Comment: Reply to the comment cond-mat/9710285 by den Hartog and van Wees; 1
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