Localization length in Dorokhov's microscopic model of multichannel wires

Abstract

We derive exact quantum expressions for the localization length $L_c$ for weak disorder in two- and three chain tight-binding systems coupled by random nearest-neighbour interchain hopping terms and including random energies of the atomic sites. These quasi-1D systems are the two- and three channel versions of Dorokhov's model of localization in a wire of $N$ periodically arranged atomic chains. We find that $L_c^{-1}=N.{\xi }^{-1}$ for the considered systems with $N=(1,2,3)$, where $\xi$ is Thouless' quantum expression for the inverse localization length in a single 1D Anderson chain, for weak disorder. The inverse localization length is defined from the exponential decay of the two-probe Landauer conductance, which is determined from an earlier transfer matrix solution of the Schrödinger equation in a Bloch basis. Our exact expressions above differ qualitatively from Dorokhov's localization length identified as the length scaling parameter in his scaling description of the distribution of the participation ratio. For N=3 we also discuss the case where the coupled chains are arranged on a strip rather than periodically on a tube. From the transfer matrix treatment we also obtain reflection coefficients matrices which allow us to find mean free paths and to discuss their relation to localization lengths in the two- and three channel systems.

References in corpus (1)

• Localization fom conductance in few-channel disordered wires

Cited by in corpus (4)

• Transport through quasi-one-dimensional wires with correlated disorder
• Mean Free Path in Disordered Multichannel Tight-Binding Wires
• Anderson localisation in two dimensions: insights from Localisation Landscape Theory, exact diagonalisation, and time-dependent simulations
• The DMPK equation for mesoscopic quantum transport revisited