Resistivity of a metal between the Boltzmann transport regime and the Anderson transition

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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.