Numerical study of conductance fluctuations in disordered metals

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Abstract
The results of a numerical study of conductance fluctuations in weakly disordered one- and two-dimensional metals are presented and compared with recent perturbative calculations. Two models are considered: the usual Anderson tight-binding model with a uniform distribution of site energies, and a second tight-binding model in which the site energies of a given concentration of ‘‘impurities’’ are ±ΔE. For the Anderson model we calculate the fluctuations of the conductance among members of an ensemble of statistically similar samples (i.e., samples with the same amount of disorder, etc.). We find that the magnitude of these fluctuations agrees fairly well with the ‘‘universal’’ value predicted by the perturbative calculations, even for systems as small as a few lattice spacings on a side. For the second model, we calculate the conductance fluctuations which occur when only a single impurity is moved, and our results are in reasonable agreement with the analytic results for this case.