A method for calculating the localisation length, with an analysis of the Lloyd model

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, , Citation R Johnston and H Kunz 1983 J. Phys. C: Solid State Phys. 16 4565 DOI 10.1088/0022-3719/16/23/018

0022-3719/16/23/4565

Abstract

A method is developed to calculate the localisation length in disordered systems. It can be considered to be a generalisation of the method of Herbert, Jones and Thouless (1971-2) for one-dimensional systems, to wires and nu -dimensional lattices. The localisation length can be calculated under some assumptions when the disorder has a Lorentzian probability distribution. No localisation transition is found, that is the localisation length is finite for arbitrarily small non-zero values of the disorder. For other distributions a perturbation expansion is developed, which is valid for large values of disorder and small energies. The dominant term and the first-order correction are calculated.

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10.1088/0022-3719/16/23/018