53 research outputs found
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
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
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
Scale-Free Networks Emerging from Weighted Random Graphs
We study Erd\"{o}s-R\'enyi random graphs with random weights associated with
each link. We generate a new ``Supernode network'' by merging all nodes
connected by links having weights below the percolation threshold (percolation
clusters) into a single node. We show that this network is scale-free, i.e.,
the degree distribution is with . Our
results imply that the minimum spanning tree (MST) in random graphs is composed
of percolation clusters, which are interconnected by a set of links that create
a scale-free tree with . We show that optimization causes the
percolation threshold to emerge spontaneously, thus creating naturally a
scale-free ``supernode network''. We discuss the possibility that this
phenomenon is related to the evolution of several real world scale-free
networks
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
Penetration of hot electrons through a cold disordered wire
We study a penetration of an electron with high energy E<<T through strongly
disordered wire of length L<<a (a being the localization length). Such an
electron can loose, but not gain the energy, when hopping from one localized
state to another. We have found a distribution function for the transmission
coefficient t. The typical t remains exponentially small in L/a, but with the
decrement, reduced compared to the case of direct elastic tunnelling. The
distribution function has a relatively strong tail in the domain of anomalously
high t; the average ~(a/L)^2 is controlled by rare configurations of
disorder, corresponding to this tail.Comment: 4 pages, 5 figure
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