From clean to diffusive mesoscopic systems: A semiclassical approach to the magnetic susceptibility

TL;DR

This paper investigates how weak disorder affects the magnetic susceptibility of mesoscopic quantum systems, bridging the gap between clean and diffusive regimes using semiclassical and diagrammatic methods.

Contribution

It introduces a combined semiclassical and diagrammatic approach to analyze spectral correlations and magnetic susceptibility in non-translational invariant mesoscopic systems with disorder.

Findings

Identifies two regimes of magnetic response depending on mean free path and inelastic scattering length.

Provides numerical results for a square billiard geometry.

Derives approximate analytic expressions for generic chaotic geometries.

Abstract

We study disorder-induced spectral correlations and their effect on the magnetic susceptibility of mesoscopic quantum systems in the non-diffusive regime. By combining a diagrammatic perturbative approach with semiclassical techniques we perform impurity averaging for non-translational invariant systems. This allows us to study the crossover from clean to diffusive systems. As an application we consider the susceptibility of non-interacting electrons in a ballistic microstructure in the presence of weak disorder. We present numerical results for a square billiard and approximate analytic results for generic chaotic geometries. We show that for the elastic mean free path $\ell$ larger than the system size, there are two distinct regimes of behaviour depending on the relative magnitudes of $\ell$ and an inelastic scattering length.