Orbital magnetic susceptibility of disordered mesoscopic systems

In this paper we study the orbital weak-field susceptibility of two-dimensional diffusive mesoscopic systems. For the previously unstudied regime of temperatures lower than the mean level spacing we find unexpected strong temperature as well as statistical ensemble dependence of the average and typical susceptibilities. An explanation for these features is given in terms of the long tail of the zero-temperature susceptibility distribution, including the parametric form of the temperature dependence. For temperatures higher than the mean level spacing we calculate the difference between the true canonical ensemble and the equivalent grand-canonical ensemble. We also perform numerical simulations, which seem to generally confirm previous theoretical predictions for this regime of temperatures, although some difficulties arise. The important role of gauge-invariance, especially how it renders the Gaussian ensembles random matrix theory inapplicable to the study of orbital susceptibility, is discussed. We conclude by considering interaction effects, giving a different interpretation to previous results as well as demonstrating the influence of in-plane magnetic field on the interaction-induced orbital response.