The magnetic susceptibility of disordered non-diffusive mesoscopic systems

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 $L_ϕ$. We present numerical results for square billiards and derive approximate analytical results for generic chaotic geometries. The magnetic field dependence and $L_ϕ$ dependence of the disorder-induced susceptibility is qualitatively similar in both types of geometry.