Numerical study of resistivity of model disordered three-dimensional metals

TL;DR

This study numerically investigates the zero-temperature resistivity of 3D disordered metals using Green's functions, revealing how different disorder types affect resistivity and localization onset.

Contribution

It provides a detailed numerical analysis of resistivity in 3D disordered metals considering both diagonal and off-diagonal disorder mechanisms, extending understanding beyond Boltzmann theory.

Findings

Resistivity is linear with sample length and varies with disorder type.

Large off-diagonal disorder leads to resistivity saturation.

Diagonal disorder causes resistivity to increase faster than Boltzmann predictions.

Abstract

We calculate the zero-temperature resistivity of model 3-dimensional disordered metals described by tight-binding Hamiltonians. Two different mechanisms of disorder are considered: diagonal and off-diagonal. The non-equilibrium 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, (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 relative to the lattice constant has a value between 0.5 and 2.0 and is strongly model dependent.