52 research outputs found
Density of states in d-wave superconductors disordered by extended impurities
The low-energy quasiparticle states of a disordered d-wave superconductor are
investigated theoretically. A class of such states, formed via tunneling
between the Andreev bound states that are localized around extended impurities
(and result from scattering between pair-potential lobes that differ in sign)
is identified. Its (divergent) contribution to the total density of states is
determined by taking advantage of connections with certain one-dimensional
random tight-binding models. The states under discussion should be
distinguished from those associated with nodes in the pair potential.Comment: 5 pages, 1 figur
Anderson transition of three dimensional phonon modes
Anderson transition of the phonon modes is studied numerically. The critical
exponent for the divergence of the localization length is estimated using the
transfer matrix method, and the statistics of the modes is analyzed. The latter
is shown to be in excellent agreement with the energy level statistics of the
disrodered electron system belonging to the orthogonal universality class.Comment: 2 pages and another page for 3 figures, J. Phys. Soc. Japa
Conductance scaling at the band center of wide wires with pure non--diagonal disorder
Kubo formula is used to get the scaling behavior of the static conductance
distribution of wide wires showing pure non-diagonal disorder. Following recent
works that point to unusual phenomena in some circumstances, scaling at the
band center of wires of odd widths has been numerically investigated. While the
conductance mean shows a decrease that is only proportional to the inverse
square root of the wire length, the median of the distribution exponentially
decreases as a function of the square root of the length. Actually, the whole
distribution decays as the inverse square root of the length except close to
G=0 where the distribution accumulates the weight lost at larger conductances.
It accurately follows the theoretical prediction once the free parameter is
correctly fitted. Moreover, when the number of channels equals the wire length
but contacts are kept finite, the conductance distribution is still described
by the previous model. It is shown that the common origin of this behavior is a
simple Gaussian statistics followed by the logarithm of the E=0 wavefunction
weight ratio of a system showing chiral symmetry. A finite value of the
two-dimensional conductance mean is obtained in the infinite size limit. Both
conductance and the wavefunction statistics distributions are given in this
limit. This results are consistent with the 'critical' character of the E=0
wavefunction predicted in the literature.Comment: 10 pages, 9 figures, RevTeX macr
Density of States of Disordered Two-Dimensional Crystals with Half-Filled Band
A diagrammatic method is applied to study the effects of commensurability in
two-dimensional disordered crystalline metals by using the particle-hole
symmetry with respect to the nesting vector P_0={\pm{\pi}/a, {\pi}/a} for a
half-filled electronic band. The density of electronic states (DoS) is shown to
have nontrivial quantum corrections due to both nesting and elastic impurity
scattering processes, as a result the van Hove singularity is preserved in the
center of the band. However, the energy dependence of the DoS is strongly
changed. A small offset from the middle of the band gives rise to disappearence
of quantum corrections to the DoS .Comment: to be published in Physical Review Letter
Density of states in the non-hermitian Lloyd model
We reconsider the recently proposed connection between density of states in
the so-called ``non-hermitian quantum mechanics'' and the localization length
for a particle moving in random potential. We argue that it is indeed possible
to find the localization length from the density of states of a non-hermitian
random ``Hamiltonian''. However, finding the density of states of a
non-hermitian random ``Hamiltonian'' remains an open problem, contrary to
previous findings in the literature.Comment: 6 pages, RevTex, two-column
Random Mass Dirac Fermions in Doped Spin-Peierls and Spin-Ladder systems: One-Particle Properties and Boundary Effects
Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized
by a gap in the spin-excitation spectrum, which can be modeled at low energies
by that of Dirac fermions with a mass. In the presence of disorder these
systems can still be described by a Dirac fermion model, but with a random
mass. Some peculiar properties, like the Dyson singularity in the density of
states, are well known and attributed to creation of low-energy states due to
the disorder. We take one step further and study single-particle correlations
by means of Berezinskii's diagram technique. We find that, at low energy
, the single-particle Green function decays in real space like
. It follows that at these energies the
correlations in the disordered system are strong -- even stronger than in the
pure system without the gap. Additionally, we study the effects of boundaries
on the local density of states. We find that the latter is logarithmically (in
the energy) enhanced close to the boundary. This enhancement decays into the
bulk as and the density of states saturates to its bulk value on
the scale . This scale is different from
the Thouless localization length . We
also discuss some implications of these results for the spin systems and their
relation to the investigations based on real-space renormalization group
approach.Comment: 26 pages, LaTex, 9 PS figures include
Effect of Substitutional Impurities on the Electronic States and Conductivity of Crystals with Half-filled Band
Low temperature quantum corrections to the density of states (DOS) and the
conductivity are examined for a two-dimensional(2D) square crystal with
substitutional impurities. By summing the leading logarithmic corrections to
the DOS its energy dependence near half-filling is obtained. It is shown that
substitutional impurities do not suppress the van Hove singularity at the
middle of the band, however they change its energy dependence strongly. Weak
disorder due to substitutional impurities in the three-dimensional simple cubic
lattice results in a shallow dip in the center of the band. The calculation of
quantum corrections to the conductivity of a 2D lattice shows that the
well-known logarithmic localization correction exists for all band fillings.
Furthermore the magnitude of the correction increases as half-filling is
approached. The evaluation of the obtained analytical results shows evidence
for delocalized states in the center of the band of a 2D lattice with
substitutional impurities
High Temperature Electron Localization in dense He Gas
We report new accurate mesasurements of the mobility of excess electrons in
high density Helium gas in extended ranges of temperature and density to ascertain
the effect of temperature on the formation and dynamics of localized electron
states. The main result of the experiment is that the formation of localized
states essentially depends on the relative balance of fluid dilation energy,
repulsive electron-atom interaction energy, and thermal energy. As a
consequence, the onset of localization depends on the medium disorder through
gas temperature and density. It appears that the transition from delocalized to
localized states shifts to larger densities as the temperature is increased.
This behavior can be understood in terms of a simple model of electron
self-trapping in a spherically symmetric square well.Comment: 23 pages, 13 figure
From Anderson to anomalous localization in cold atomic gases with effective spin-orbit coupling
We study the dynamics of a one-dimensional spin-orbit coupled Schrodinger
particle with two internal components moving in a random potential. We show
that this model can be implemented by the interaction of cold atoms with
external lasers and additional Zeeman and Stark shifts. By direct numerical
simulations a crossover from an exponential Anderson-type localization to an
anomalous power-law behavior of the intensity correlation is found when the
spin-orbit coupling becomes large. The power-law behavior is connected to a
Dyson singularity in the density of states emerging at zero energy when the
system approaches the quasi-relativistic limit of the random mass Dirac model.
We discuss conditions under which the crossover is observable in an experiment
with ultracold atoms and construct explicitly the zero-energy state, thus
proving its existence under proper conditions.Comment: 4 pages and 4 figure
Zero-modes in the random hopping model
If the number of lattice sites is odd, a quantum particle hopping on a
bipartite lattice with random hopping between the two sublattices only is
guaranteed to have an eigenstate at zero energy. We show that the localization
length of this eigenstate depends strongly on the boundaries of the lattice,
and can take values anywhere between the mean free path and infinity. The same
dependence on boundary conditions is seen in the conductance of such a lattice
if it is connected to electron reservoirs via narrow leads. For any nonzero
energy, the dependence on boundary conditions is removed for sufficiently large
system sizes.Comment: 12 pages, 11 figure
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