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 $\epsilon$, the single-particle Green function decays in real space like $G(x,\epsilon) \propto (1/x)^{3/2}$. 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 $1/\sqrt{x}$ and the density of states saturates to its bulk value on the scale $L_\epsilon \propto \ln^2 (1/\epsilon)$. This scale is different from the Thouless localization length $\lambda_\epsilon\propto\ln (1/\epsilon)$. 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 $[(26\leq T\leq 77) K ]$ and density $[ (0.05\leq N\leq 12.0) {atoms} \cdot {nm}^{-3}]$ 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

Spectral Statistics in Chiral-Orthogonal Disordered Systems

We describe the singularities in the averaged density of states and the corresponding statistics of the energy levels in two- (2D) and three-dimensional (3D) chiral symmetric and time-reversal invariant disordered systems, realized in bipartite lattices with real off-diagonal disorder. For off-diagonal disorder of zero mean we obtain a singular density of states in 2D which becomes much less pronounced in 3D, while the level-statistics can be described by semi-Poisson distribution with mostly critical fractal states in 2D and Wigner surmise with mostly delocalized states in 3D. For logarithmic off-diagonal disorder of large strength we find indistinguishable behavior from ordinary disorder with strong localization in any dimension but in addition one-dimensional $1/|E|$ Dyson-like asymptotic spectral singularities. The off-diagonal disorder is also shown to enhance the propagation of two interacting particles similarly to systems with diagonal disorder. Although disordered models with chiral symmetry differ from non-chiral ones due to the presence of spectral singularities, both share the same qualitative localization properties except at the chiral symmetry point E=0 which is critical.Comment: 13 pages, Revtex file, 8 postscript files. It will appear in the special edition of J. Phys. A for Random Matrix Theor