Journal of Experimental and Theoretical Physics

, Volume 96, Issue 2, pp 355–382 | Cite as

Density of prelocalized states in mesoscopic NS systems

  • P. M. Ostrovsky
  • M. A. Skvortsov
  • M. V. Feigel’man
Reviews

Abstract

The semiclassical theory of the proximity effect predicts the formation of a gap Eg∼ℏD/L2 in the excitation spectrum of a diffusive contact between a normal metal and a superconductor (NS). Mesoscopic fluctuations lead to the emergence of states localized anomalously in the normal metal and weakly linked with the superconducting bank, creating a nonzero density of states for energies lower than Eg. In this review, the behavior of the density of quasiparticle states below a quasi-classical gap is considered for various geometries of the NS system (special attention is paid to SNS junctions) and for the problem of a superconductor with a low concentration of magnetic impurities, in which a similar effect is observed. Analysis is mainly carried out on the basis of a fully microscopic method of the supermatrix σ model; in this method, a nonzero density of states emerges due to instanton configurations with broken supersymmetry. In addition, the results of an alternative approach proceeding from the idea of universality of the spectra of random Hamiltonians with the given symmetry are reviewed. In situations studied using both methods, the results are identical. They include the exact expression for the mean density of states of an NS system in the vicinity of Eg. In the framework of 1D and 2D σ models, the subgap density of states is determined with an exponential accuracy. The contacts with a poor transparency of the NS interface are also considered. It is shown that the number of subgap states in the case of low transparency is much greater than unity.

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Copyright information

© MAIK "Nauka/Interperiodica" 2003

Authors and Affiliations

  • P. M. Ostrovsky
    • 1
  • M. A. Skvortsov
    • 1
  • M. V. Feigel’man
    • 1
  1. 1.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia

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