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Publication Office of Progress of Theoretical Physics, Progress of Theoretical Physics -- Supplement-, (166), p. 136-142

DOI: 10.1143/ptps.166.136

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Precise asymptotics for a variable-range hopping model

Journal article published in 2007 by Bernhard Mehlig ORCID, Michael Wilkinson
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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Abstract

For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse. Here we give precise asymptotic results for a modified variable-range hopping model, proposed by S. Alexander [Phys. Rev. B, 26, 2956 (1982)]. If a system has localised electron states the DC conductivity must be zero at zero temperature, but localised electrons can conduct at finite temperatures. Mott 1) proposed that the low-temperature dependence of the DC conductivity is