Anderson localization from the replica formalism

We study Anderson localization in quasi-one-dimensional disordered wires within the framework of the replica sigma model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons, and Zirnbauer, we com...

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Bibliographic Details
Published in:Physical review letters 2005-11, Vol.95 (20), p.206601.1-206601.4, Article 206601
Main Authors: ALTLAND, Alexander, KARNENEV, Alex, CHUSHUN TIAN
Format: Article
Language:English
Subjects:
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Electronic structure and electrical properties of surfaces, interfaces, thin films and low-dimensional structures
Exact sciences and technology
Localization effects (anderson or weak localization)
Physics
Surface and interface electron states
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Summary:We study Anderson localization in quasi-one-dimensional disordered wires within the framework of the replica sigma model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the context of supersymmetry by Lamacraft, Simons, and Zirnbauer, we compute the exact density of transmission matrix eigenvalues of superconducting wires (of symmetry class CI.) For the unitary class of metallic systems (class A) we are able to obtain the density function, save for its large transmission tail.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.95.206601