68 research outputs found
Quantum percolation in granular metals
Theory of quantum corrections to conductivity of granular metal films is
developed for the realistic case of large randomly distributed tunnel
conductances. Quantum fluctuations of intergrain voltages (at energies E much
below bare charging energy scale E_C) suppress the mean conductance \bar{g}(E)
much stronger than its standard deviation \sigma(E). At sufficiently low
energies E_* any distribution becomes broad, with \sigma(E_*) ~ \bar{g}(E_*),
leading to strong local fluctuations of the tunneling density of states.
Percolative nature of metal-insulator transition is established by combination
of analytic and numerical analysis of the matrix renormalization group
equations.Comment: 6 pages, 5 figures, REVTeX
Anomalous Josephson current via Majorana bound states in topological insulators
We propose a setup involving Majorana bound states (MBS) hosted by a vortex
on a superconducting surface of a 3D Topological Insulator (TI). We consider a
narrow channel drilled across a TI slab with both sides covered by s-wave
superconductor. In the presence of a vortex pinned to such a channel, it acts
as a ballistic nanowire connecting the superconducting surfaces, with a pair of
MBS localized in it. The energies of the MBS possess a 4\pi-periodic dependence
on the superconductive phase difference \phi between the surfaces. It results
in the appearence of an anomalous term in the current-phase relation, I_a(\phi)
for the supercurrent flowing along the channel between the superconductive
surfaces. We have calculated the shape of the 4\pi-periodic function I_a(\phi),
as well as the dependence of its amplitude on temperature and system
parameters.Comment: 7 pages, 3 figure
Protected Qubits and Chern Simons theories in Josephson Junction Arrays
We present general symmetry arguments that show the appearance of doubly
denerate states protected from external perturbations in a wide class of
Hamiltonians. We construct the simplest spin Hamiltonian belonging to this
class and study its properties both analytically and numerically. We find that
this model generally has a number of low energy modes which might destroy the
protection in the thermodynamic limit. These modes are qualitatively different
from the usual gapless excitations as their number scales as the linear size
(instead of volume) of the system. We show that the Hamiltonians with this
symmetry can be physically implemented in Josephson junction arrays and that in
these arrays one can eliminate the low energy modes with a proper boundary
condition. We argue that these arrays provide fault tolerant quantum bits.
Further we show that the simplest spin model with this symmetry can be mapped
to a very special Z_2 Chern-Simons model on the square lattice. We argue that
appearance of the low energy modes and the protected degeneracy is a natural
property of lattice Chern-Simons theories. Finally, we discuss a general
formalism for the construction of discrete Chern-Simons theories on a lattice.Comment: 20 pages, 7 figure
Phase Transition in a Self-repairing Random Network
We consider a network, bonds of which are being sequentially removed; that is
done at random, but conditioned on the system remaining connected
(Self-Repairing Bond Percolation SRBP). This model is the simplest
representative of a class of random systems for which forming of isolated
clusters is forbidden. It qualitatively describes the process of fabrication of
artificial porous materials and degradation of strained polymers. We find a
phase transition at a finite concentration of bonds , at which the
backbone of the system vanishes; for all the network is a dense
fractal.Comment: 4 pages, 4 figure
Universality and non-universality in behavior of self-repairing random networks
We numerically study one-parameter family of random single-cluster systems. A
finite-concentration topological phase transition from the net-like to the
tree-like phase (the latter is without a backbone) is present in all models of
the class. Correlation radius index of the backbone in the net-like
phase; graph dimensions -- of the tree-like phase, and of
the backbone in the net-like phase appear to be universal within the accuracy
of our calculations, while the backbone fractal dimension is not
universal: it depends on the parameter of a model.Comment: Published variant; more accurate numerical data and minor
corrections. 4 pages, 5 figure
Percolation with excluded small clusters and Coulomb blockade in a granular system
We consider dc-conductivity of a mixture of small conducting and
insulating grains slightly below the percolation threshold, where finite
clusters of conducting grains are characterized by a wide spectrum of sizes.
The charge transport is controlled by tunneling of carriers between neighboring
conducting clusters via short ``links'' consisting of one insulating grain.
Upon lowering temperature small clusters (up to some -dependent size) become
Coulomb blockaded, and are avoided, if possible, by relevant hopping paths. We
introduce a relevant percolational problem of next-nearest-neighbors (NNN)
conductivity with excluded small clusters and demonstrate (both numerically and
analytically) that decreases as power law of the size of excluded
clusters. As a physical consequence, the conductivity is a power-law function
of temperature in a wide intermediate temperature range. We express the
corresponding index through known critical indices of the percolation theory
and confirm this relation numerically.Comment: 7 pages, 6 figure
Universal temperature dependence of the conductivity of a strongly disordered granular metal
A disordered array of metal grains with large and random intergrain
conductances is studied within the one-loop accuracy renormalization group
approach. While at low level of disorder the dependence of conductivity on log
T is nonuniversal (it depends on details of the array's geometry), for strong
disorder this dependence is described by a universal nonlinear function, which
depends only on the array's dimensionality. In two dimensions this function is
found numerically. The dimensional crossover in granular films is discussed.Comment: 6 pages, 6 figures, submitted to JETP Letter
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