96 research outputs found
Coexistence of localized and extended states in the Anderson model with long-range hopping
We study states arising from fluctuations in the disorder potential in
systems with long-range hopping. Here, contrary to systems with short-range
hopping, the optimal fluctuations of disorder responsible for the formation of
the states in the gap, are not rendered shallow and long-range when
approaches the band edge (). Instead, they remain deep and short-range.
The corresponding electronic wave functions also remain short-range-localized
for all . This behavior has striking implications for the structure of the
wave functions slightly above . By a study of finite systems, we
demonstrate that the wave functions transform from a localized to a
quasi-localized type upon crossing the level, forming resonances embedded
in the continuum. The quasi-localized consists of a
short-range core that is essentially the same as and a delocalized
tail extending to the boundaries of the system. The amplitude of the tail is
small, but it decreases with slowly. Its contribution to the norm of the
wave function dominates for sufficiently large system sizes, ;
such states behave as delocalized ones. In contrast, in small systems, , quasi-localized states are overwhelmingly dominated by the localized
cores and are effectively localized.Comment: 18+1 pages, 9+1 figure
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
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