Analysis of negative magnetoresistance. Statistics of closed paths. I. Theory

TL;DR

This paper uses computer simulations to analyze how closed paths in 2D systems affect quantum interference corrections to conductivity and magnetoconductance, considering both ballistic and diffusive regimes.

Contribution

It demonstrates that anomalous magnetoconductance can be modeled with diffusion approximation formulas, adjusting parameters like prefactor and phase-breaking length.

Findings

Simulation results align with diffusion approximation models

Prefactor in the magnetoconductance expression is less than one

Phase-breaking length differs from the true value in the model

Abstract

Statistics of closed paths in two-dimensional (2D) systems, which just determines the interference quantum correction to conductivity and anomalous magnetoconductance, has been studied by computer simulation of a particle motion over the plane with randomly distributed scatterers. Both ballistic and diffusion regimes have been considered. The results of simulation have been analyzed in the framework of diffusion approximation. They are used for calculation of the magnetic field dependence of magnetoconductance in the model 2D system. It is shown that the anomalous magnetoconductance can be in principle described by the well known expression, obtained in the diffusion approximation, but with the prefactor less than unity and phase breaking length which differs from true value.