Percolation and one- to three-dimensional cross-over in the Anderson localisation

Abstract

The authors consider a system composed of a random network of quasi-one-dimensional (1D) multichannel conductors. The zero- and finite-temperature (T) behaviour of the conductivity are studied, and the dependence on the impurity concentration ( eta ) is indicated. A very rich behaviour is found, depending on the various length scales of the problem. In general the conductivity of the system is 'classical' at high temperatures. At lower T it reflects 1D localisation effects, and then crosses over to a 3D regime. In some cases a percolative-type metal-insulator transition may take over. They indicate possible experimental realisations of their system.