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

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 larger than the system size, there are two distinct regimes of behaviour depending on the relative magnitudes of and an inelastic scattering length.