Resistivity of a Metal between the Boltzmann Transport Regime and the Anderson Transition

Abstract

We study the transport properties of a finite three dimensional disordered conductor, for both weak and strong scattering on impurities, employing the real-space Green function technique and related Landauer-type formula. The dirty metal is described by a nearest neighbor tight-binding Hamiltonian with a single s-orbital per site and random on-site potential (Anderson model). We compute exactly the zero-temperature conductance of a finite size sample placed between two semi-infinite disorder-free leads. The resistivity is found from the coefficient of linear scaling of the disorder averaged resistance with sample length. This ``quantum'' resistivity is compared to the semiclassical Boltzmann expression computed in both Born approximation and multiple scattering approximation.