Correlations of the local density of states in quasi-one-dimensional wires

We report a calculation of the correlation function of the local density of states in a disordered quasi-one-dimensional wire in the unitary symmetry class at a small energy difference. Using an expression from the supersymmetric sigma-model, we obtain the full dependence of the two-point correlation function on the distance between the points. In the limit of zero energy difference, our calculation reproduces the statistics of a single localized wave function. At logarithmically large distances of the order of the Mott scale, we obtain a reentrant behavior similar to that in strictly one-dimensional chains.Comment: Published version. Minor technical and notational improvements. 16 pages, 1 figur

Density of States in a Mesoscopic SNS Junction

Semiclassical theory of proximity effect predicts a gap E_g \sim hD/L^2 in the excitation spectrum of a long diffusive SNS junction. Mesoscopic fluctuations lead to anomalously localized states in the normal part of the junction. As a result, a non-zero, yet exponentially small, density of states appears at energies below E_g. In the framework of the supermatrix nonlinear sigma-model these prelocalized states are due to instanton configurations with broken supersymmetry. The exact result for the DOS near the semiclassical threshold is found provided the dimensionless conductance of the normal part is large. The case of poorly transparent interfaces between the normal and superconductive regions is also considered. In this limit the total number of the subgap states may be large.Comment: 6 pages, 2 eps figures, JETP Letters style file include

Anderson localization on random regular graphs

A numerical study of Anderson transition on random regular graphs (RRG) with diagonal disorder is performed. The problem can be described as a tight-binding model on a lattice with N sites that is locally a tree with constant connectivity. In certain sense, the RRG ensemble can be seen as infinite-dimensional ($d\to\infty$) cousin of Anderson model in d dimensions. We focus on the delocalized side of the transition and stress the importance of finite-size effects. We show that the data can be interpreted in terms of the finite-size crossover from small ($N\ll N_c$) to large ($N\gg N_c$) system, where $N_c$ is the correlation volume diverging exponentially at the transition. A distinct feature of this crossover is a nonmonotonicity of the spectral and wavefunction statistics, which is related to properties of the critical phase in the studied model and renders the finite-size analysis highly non-trivial. Our results support an analytical prediction that states in the delocalized phase (and at $N\gg N_c$) are ergodic in the sense that their inverse participation ratio scales as $1/N$

Proximity Action theory of superconductive nanostructures

We review a novel approach to the superconductive proximity effect in disordered normal-superconducting (N-S) structures. The method is based on the multicharge Keldysh action and is suitable for the treatment of interaction and fluctuation effects. As an application of the formalism, we study the subgap conductance and noise in two-dimensional N-S systems in the presence of the electron-electron interaction in the Cooper channel. It is shown that singular nature of the interaction correction at large scales leads to a nonmonotonuos temperature, voltage and magnetic field dependence of the Andreev conductance.Comment: RevTeX, 6 pages, 5 eps figures. This is a concise review of cond-mat/0008463; to be published in the Proceedings of the conference "Mesoscopic and strongly correlated electron systems" (Chernogolovka, Russia, July 2000