1,137 research outputs found
Effect of Strong Disorder in a 3-Dimensional Topological Insulator: Phase Diagram and Maps of the Z2 Invariant
We study the effect of strong disorder in a 3-dimensional topological
insulators with time-reversal symmetry and broken inversion symmetry. Firstly,
using level statistics analysis, we demonstrate the persistence of delocalized
bulk states even at large disorder. The delocalized spectrum is seen to display
the levitation and pair annihilation effect, indicating that the delocalized
states continue to carry the Z2 invariant after the onset of disorder.
Secondly, the Z2 invariant is computed via twisted boundary conditions using an
efficient numerical algorithm. We demonstrate that the Z2 invariant remains
quantized and non-fluctuating even after the spectral gap becomes filled with
dense localized states. In fact, our results indicate that the Z2 invariant
remains quantized until the mobility gap closes or until the Fermi level
touches the mobility edges. Based on such data, we compute the phase diagram of
the Bi2Se3 topological material as function of disorder strength and position
of the Fermi level.Comment: references added; final versio
Cross-over from retro to specular Andreev reflections in bilayer graphene
Ongoing experimental progress in the preparation of ultra-clean
graphene/superconductor (SC) interfaces enabled the recent observation of
specular interband Andreev reflections (AR) at bilayer graphene
(BLG)/NbSe van der Waals interfaces [Nature Physics 12, (2016)].
Motivated by this experiment we theoretically study the differential
conductance across a BLG/SC interface at the continuous transition from high to
ultra-low Fermi energies in BLG. Using the Bogoliubov-deGennes
equations and the Blonder-Tinkham-Klapwijk formalism we derive analytical
expressions for the differential conductance across the BLG/SC interface. We
find a characteristic signature of the cross-over from intra-band retro- (high
) to inter-band specular (low ) ARs, that manifests itself in a
strongly suppressed interfacial conductance when the excitation energy
(the SC gap). The sharpness of these
conductance dips is strongly dependent on the size of the potential step at the
BLG/SC interface
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
Transition from insulating to a non-insulating temperature dependence of the conductivity in granular metals
We consider interaction effects in a granular normal metal at not very low
temperatures. Assuming that all weak localization effects are suppressed by the
temperature we replace the initial Hamiltonian by a proper functional of phases
and study the possibility for a phase transition depending on the tunneling
conductance . It is demonstrated for any dimension that, while at small
the conductivity decays with temperature exponentially, its temperature
dependence is logarithmic at large The formulae obtained are compared with
an existing experiment and a good agreement is found.Comment: 9 pages, a mistake is corrected and several formulae adde
Supersymmetry for disordered systems with interaction
Considering disordered electron systems we suggest a scheme that allows us to
include an electron-electron interaction into a supermatrix sigma-model. The
method is based on replacing the initial model of interacting electons by a
fully supersymmetric model. Although this replacement is not exact, it is a
good approximation for a weak short range interaction and arbitrary disorder.
The replacement makes the averaging over disorder and further manipulations
straightforward and we come to a supermatrix sigma-model containing an
interaction term. The structure of the model is rather similar to the replica
one, although the interaction term has a different form. We study the model
making perturbation theory and renormalization group calculations. We check the
renormalizability of the model in the first loop approximation and in the first
order in the interaction. In this limit we reproduce the renormalization group
equations known from earlier works. We hope that the new supermatrix
sigma-model may become a new tool for non-perturbative calculations for
disordered systems with interaction.Comment: 18 pages, 8 figures, published version with minor change
A semiclassical theory of the Anderson transition
We study analytically the metal-insulator transition in a disordered
conductor by combining the self-consistent theory of localization with the one
parameter scaling theory. We provide explicit expressions of the critical
exponents and the critical disorder as a function of the spatial
dimensionality, . The critical exponent controlling the divergence of
the localization length at the transition is found to be . This result confirms that the upper critical dimension is
infinity. Level statistics are investigated in detail. We show that the two
level correlation function decays exponentially and the number variance is
linear with a slope which is an increasing function of the spatial
dimensionality.Comment: 4 pages, journal versio
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