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

Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator

We investigate the quasiparticle density of states in disordered d-wave superconductors. By constructing a quantum map describing the quasiparticle dynamics in such a medium, we explore deviations of the density of states from its universal form ($\propto E$), and show that additional low-energy quasiparticle states exist provided (i) the range of the impurity potential is much larger than the Fermi wavelength [allowing to use recently developed semiclassical methods]; (ii) classical trajectories exist along which the pair-potential changes sign; and (iii) the diffractive scattering length is longer than the superconducting coherence length. In the classically chaotic regime, universal random matrix theory behavior is restored by quantum dynamical diffraction which shifts the low energy states away from zero energy, and the quasiparticle density of states exhibits a linear pseudogap below an energy threshold $E^* \ll \Delta_0$.Comment: 4 pages, 3 figures, RevTe

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

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

Bosonic Excitations in Random Media

We consider classical normal modes and non-interacting bosonic excitations in disordered systems. We emphasise generic aspects of such problems and parallels with disordered, non-interacting systems of fermions, and discuss in particular the relevance for bosonic excitations of symmetry classes known in the fermionic context. We also stress important differences between bosonic and fermionic problems. One of these follows from the fact that ground state stability of a system requires all bosonic excitation energy levels to be positive, while stability in systems of non-interacting fermions is ensured by the exclusion principle, whatever the single-particle energies. As a consequence, simple models of uncorrelated disorder are less useful for bosonic systems than for fermionic ones, and it is generally important to study the excitation spectrum in conjunction with the problem of constructing a disorder-dependent ground state: we show how a mapping to an operator with chiral symmetry provides a useful tool for doing this. A second difference involves the distinction for bosonic systems between excitations which are Goldstone modes and those which are not. In the case of Goldstone modes we review established results illustrating the fact that disorder decouples from excitations in the low frequency limit, above a critical dimension $d_c$, which in different circumstances takes the values $d_c=2$ and $d_c=0$. For bosonic excitations which are not Goldstone modes, we argue that an excitation density varying with frequency as $\rho(\omega) \propto \omega^4$ is a universal feature in systems with ground states that depend on the disorder realisation. We illustrate our conclusions with extensive analytical and some numerical calculations for a variety of models in one dimension

Network models for localisation problems belonging to the chiral symmetry classes

We consider localisation problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behaviour at a band centre. We formulate models which have the relevant symmetries and which are generalisations of the network model introduced previously in the context of the integer quantum Hall plateau transition. We show that the generalisations required can be re-expressed as corresponding to the introduction of absorption and amplification into either the original network model, or the variants of it that represent disordered superconductors. In addition, we demonstrate that by imposing appropriate constraints on disorder, a lattice version of the Dirac equation with a random vector potential can be obtained, as well as new types of critical behaviour. These models represent a convenient starting point for analytic discussions and computational studies, and we investigate in detail a two-dimensional example without time-reversal invariance. It exhibits both localised and critical phases, and band-centre singularities in the critical phase approach more closely in small systems the expected asymptotic form than in other known realisations of the symmetry class.Comment: 14 pages, 15 figures, Submitted to Physical Review

Percolation thresholds in chemical disordered excitable media

The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the light-sensitive Belousov-Zhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed, which depend on the relative wave transmittances of the two-state medium considered

Disorder-assisted error correction in Majorana chains

It was recently realized that quenched disorder may enhance the reliability of topological qubits by reducing the mobility of anyons at zero temperature. Here we compute storage times with and without disorder for quantum chains with unpaired Majorana fermions - the simplest toy model of a quantum memory. Disorder takes the form of a random site-dependent chemical potential. The corresponding one-particle problem is a one-dimensional Anderson model with disorder in the hopping amplitudes. We focus on the zero-temperature storage of a qubit encoded in the ground state of the Majorana chain. Storage and retrieval are modeled by a unitary evolution under the memory Hamiltonian with an unknown weak perturbation followed by an error-correction step. Assuming dynamical localization of the one-particle problem, we show that the storage time grows exponentially with the system size. We give supporting evidence for the required localization property by estimating Lyapunov exponents of the one-particle eigenfunctions. We also simulate the storage process for chains with a few hundred sites. Our numerical results indicate that in the absence of disorder, the storage time grows only as a logarithm of the system size. We provide numerical evidence for the beneficial effect of disorder on storage times and show that suitably chosen pseudorandom potentials can outperform random ones.Comment: 50 pages, 7 figure

Position des bandes d'énergie d'un alliage binaire dans l'approximation du potentiel auto-cohérent

In the single site approximation of the CPA for a completely disordered binary alloy, the band edges and the condition for the splitting of the bands in the alloy can be found without solving iteratively the Soven equation for the self-energy. The band limits are simply determined by the intersections of a universal curve characteristic of the crystalline structure under consideration and of a straight line, the slope and the ordinate at the origin of which depend only üpon the alloy concentration and the atomic energy levels of both components.Nous montrons que dans l'approximation à un site du potentiel auto-cohérent pour un alliage binaire totalement désordonné, il n'est pas nécessaire d'effectuer le calcul itératif de la self-énergie pour déterminer les limites de bandes de l'alliage et la condition de séparation des bandes. Les bords de bandes sont déterminés simplement par les intersections d'une courbe universelle propre à la structure cristalline considérée et d'une droite dont la pente et l'ordonnée à l'origine ne dépendent que de la concentration de l'alliage et de la séparation des niveaux d'énergie atomiques des deux composants