Conductance fluctuations in disordered systems: Dependence on the degree of disorder

Numerical methods have been used to study conductance fluctuations in disordered tight-binding models. The distributions of the conductance, G, for ensembles of systems with different amounts of disorder, energy, etc., have been calculated. For the case of weak disorder we find that the second moment of the distribution, var(G)≡〈$G^2$〉-〈G${〉}^2$, is in good agreement with the universal value predicted by perturbative calculations, var(G)≊($e^2$/h${)}^2$. As the amount of disorder is increased and 〈G〉 is reduced below ≊$e^2$/h, we find that var(G) is reduced below the universal value. In agreement with recent predictions, it is found that the variation of var(G) with 〈G〉 appears to be a universal function of 〈G〉, even for small 〈G〉. That is, there seems to be a simple relation between var(G) and 〈G〉, which is independent of system size, and the various parameters in the Hamiltonian. We also calculate higher moments of the conductance distribution, and discuss quantitatively the behavior of the conductance distribution. While most of our calculations have concerned two-dimensional systems, we have found that var(G) is also a universal function of 〈G〉 in one dimension. In fact, the relation between var(G) and 〈G〉, for 〈G〉≲$e^2$/h, appears to be the same in one and two dimensions. This ‘‘super’’-universality is not predicted by the perturbative calculations. Finally, we have searched for the predicted nonuniversality of the higher moments of the conductance distribution, but to within our uncertainties we find that these moments do appear to be universal functions of 〈G〉.