928 research outputs found
Topology of Bands in Solids : From Insulators to Dirac Matter
Bloch theory describes the electronic states in crystals whose energies are
distributed as bands over the Brillouin zone. The electronic states
corresponding to a (few) isolated energy band(s) thus constitute a vector
bundle. The topological properties of these vector bundles provide new
characteristics of the corresponding electronic phases. We review some of these
properties in the case of (topological) insulators and semi-metals.Comment: Talk at Seminaire Poincare (Bourbaphy), Paris, June 2014,
www.bourbaphy.f
Universal metallic and insulating properties of one dimensional Anderson Localization : a numerical Landauer study
We present results on the Anderson localization in a quasi one-dimensional
metallic wire in the presence of magnetic impurities. We focus within the same
numerical analysis on both the universal localized and metallic regimes, and we
study the evolution of these universal properties as the strength of the
magnetic disorder is varied. For this purpose, we use a numerical Landauer
approach, and derive the scattering matrix of the wire from electron's Green's
function obtained from a recursive algorithm
An Introduction to Topological Insulators
Electronic bands in crystals are described by an ensemble of Bloch wave
functions indexed by momenta defined in the first Brillouin Zone, and their
associated energies. In an insulator, an energy gap around the chemical
potential separates valence bands from conduction bands. The ensemble of
valence bands is then a well defined object, which can possess non-trivial or
twisted topological properties. In the case of a twisted topology, the
insulator is called a topological insulator. We introduce this notion of
topological order in insulators as an obstruction to define the Bloch wave
functions over the whole Brillouin Zone using a single phase convention.
Several simple historical models displaying a topological order in dimension
two are considered. Various expressions of the corresponding topological index
are finally discussed.Comment: 46 pages, 29 figures. This papers aims to be a pedagogical review on
topological insulators. It was written for the topical issue of "Comptes
Rendus de l'Acad\'emie des Sciences - Physique" devoted to topological
insulators and Dirac matte
Conductance correlations in a mesoscopic spin glass wire : a numerical Landauer study
In this letter we study the coherent electronic transport through a metallic
nanowire with magnetic impurities. The spins of these impurities are considered
as frozen to mimic a low temperature spin glass phase. The transport properties
of the wire are derived from a numerical Landauer technique which provides the
conductance of the wire as a function of the disorder configuration. We show
that the correlation of conductance between two spin configurations provides a
measure of the correlation between these spin configurations. This correlation
corresponds to the mean field overlap in the absence of any spatial order
between the spin configurations. Moreover, we find that these conductance
correlations are sensitive to the spatial order between the two spin
configurations, i.e whether the spin ?ips between them occur in a compact
region or not
Glass phase of two-dimensional triangular elastic lattices with disorder
We study two dimensional triangular elastic lattices in a background of point
disorder, excluding dislocations (tethered network). Using both (replica
symmetric) static and (equilibrium) dynamic renormalization group for the
corresponding component model, we find a transition to a glass phase for
, described by a plane of perturbative fixed points. The growth of
displacements is found to be asymptotically isotropic with , with universal subdominant anisotropy . where and depend continuously on temperature and the
Poisson ratio . We also obtain the continuously varying dynamical
exponent . For the Cardy-Ostlund model, a particular case of the above
model, we point out a discrepancy in the value of with other published
results in the litterature. We find that our result reconciles the order of
magnitude of the RG predictions with the most recent numerical simulations.Comment: 25 pages, RevTeX, uses epsf,multicol and amssym
Parallel Transport and Band Theory in Crystals
We show that different conventions for Bloch Hamiltonians on non-Bravais
lattices correspond to different natural definitions of parallel transport of
Bloch eigenstates. Generically the Berry curvatures associated with these
parallel transports differ, while physical quantities are naturally related to
a canonical choice of the parallel transport.Comment: 5 pages, 1 figure ; minor updat
Topological Weyl Semi-metal from a Lattice Model
We define and study a three dimensional lattice model which displays a Weyl
semi-metallic phase. This model consists of coupled layers of quantum
(anomalous) Hall insulators. The Weyl semi-metallic phase appears between a
resulting quantum Hall insulating phase and a normal insulating phase. Weyl
fermions in this Weyl semi-metal, similar to Dirac fermions in graphene, have
their lattice pseudo-spin locked to their momenta. We investigate surface
states and Fermi arcs, and their evolution for different phases, by exactly
diagonalizing the lattice model as well as by analyzing their topological
origins.Comment: Accepted version for publication in EPL. 6 pages, 4 figure
On the disorder-driven quantum transition in three-dimensional relativistic metals
The Weyl semimetals are topologically protected from a gap opening against
weak disorder in three dimensions. However, a strong disorder drives this
relativistic semimetal through a quantum transition towards a diffusive
metallic phase characterized by a finite density of states at the band
crossing. This transition is usually described by a perturbative
renormalization group in of a Gross-Neveu model in the
limit . Unfortunately, this model is not multiplicatively
renormalizable in dimensions: An infinite number of relevant
operators are required to describe the critical behavior. Hence its use in a
quantitative description of the transition beyond one-loop is at least
questionable. We propose an alternative route, building on the correspondence
between the Gross-Neveu and Gross-Neveu-Yukawa models developed in the context
of high energy physics. It results in a model of Weyl fermions with a random
non-Gaussian imaginary potential which allows one to study the critical
properties of the transition within a expansion. We also
discuss the characterization of the transition by the multifractal spectrum of
wave functions.Comment: 5+8 pages, 1+5 figure
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