Disordered one-dimensional conductors at finite temperature

Inelastic scattering processes at nonzero temperatures produce a broadening, h/τin, of electronic energies which essentially is equivalent to the imaginary component of the energy one must introduce in order to evaluate the Kubo formula for the d.c. conductivity of a dirty metal. We1) have developed a fast algorithm for evaluating the conductivity of a linear chain, and have used it to study the dependence of the conductivity on the magnitude of the imaginary part of the electron energy. Results for the Anderson model with different degrees of disorder and at different energies can all be scaled onto the same curve, which is of the form expected from the usual theory of localized states. A cross-over is evident between two limiting regimes: in one the damping caused by the complex energy is dominant; in the other, localization of the eigenstates dominates. The universal curve obtained make it possible to connect tight binding model results with the conductivity calculated for an electron in a white noise potential. This curve describes models in which the scattering potentials have finite variance. Similar, but not identical, results are obtained for tight binding chains with a Cauchy distribution of site energies. © 1981.