The magnetic susceptibility of disordered non-diffusive mesoscopic systems

TL;DR

This paper investigates how disorder affects the magnetic susceptibility of mesoscopic quantum systems across different regimes, combining diagrammatic and semiclassical methods to analyze spectral correlations and magnetic responses.

Contribution

It introduces a unified approach to study spectral correlations and magnetic susceptibility in disordered mesoscopic systems from clean to diffusive regimes, including analytical and numerical results.

Findings

Existence of two regimes in ballistic systems depending on mean free path and inelastic length.

Magnetic susceptibility shows similar dependence on disorder and field in different geometries.

Numerical results for square billiards support analytical approximations.

Abstract

Disorder-induced spectral correlations of mesoscopic quantum systems in the non-diffusive regime and their effect on the magnetic susceptibility are studied. We perform impurity averaging for non-translational invariant systems by combining a diagrammatic perturbative approach with semiclassical techniques. This allows us to study the entire range from clean to diffusive systems. As an application we consider the magnetic response of non-interacting electrons in microstructures in the presence of weak disorder. We show that in the ballistic case (elastic mean free path $\ell$ larger than the system size) there exist two distinct regimes of behaviour depending on the relative magnitudes of $\ell$ and an inelastic scattering length $L_{\phi}$. We present numerical results for square billiards and derive approximate analytical results for generic chaotic geometries. The magnetic field dependence and $L_{\phi}$ dependence of the disorder-induced susceptibility is qualitatively similar in both types of geometry.