Numerical resistivity calculations for disordered three-dimensional metal models using tight-binding Hamiltonians

Abstract

We calculate the zero-temperature resistivity of model three-dimensional disordered metals described by tight-binding Hamiltonians. Two different mechanisms of disorder are considered: diagonal disorder (random on-site potentials) and off-diagonal disorder (random hopping integrals). The nonequilibrium Green function formalism provides a Landauer-type formula for the conductance of arbitrary mesoscopic systems. We use this formula to calculate the resistance of finite-size disordered samples of different lengths. The resistance averaged over disorder configurations is linear in sample length and resistivity is found from the coefficient of proportionality. Two structures are considered: (1) a simple cubic lattice with one s-orbital per site, and (2) a simple cubic lattice with two d-orbitals. For small values of the disorder strength, our results agree with those obtained from the Boltzmann equation. Large off-diagonal disorder causes the resistivity to saturate, whereas increasing diagonal disorder causes the resistivity to increase faster than the Boltzmann result. The crossover toward localization starts when the Boltzmann mean free path l relative to the lattice constant a has a value between 0.5 and 2.0 and is strongly model dependent.