Theory of Landau diamagnetism of dirty metals

Abstract

We give a linear-response formulation of the Landau diamagnetism in a dirty metal featuring the disorder-unaveraged diamagnetic susceptibility tensor. Upon averaging over the disorder, we obtain the well-known result that the average susceptibility of a disordered metal is identical to that of a clean metal. We also determine the correlation function of the susceptibility tensor and show that the average mesoscopic fluctuation of the susceptibility can be up to (${\mathrm{\ensuremath{\varepsilon}}}_{\mathit{F}}$\ensuremath{\tau}${)}^{2}$ times larger than its average value. We interpret this effect in terms of the diffusive nature of the orbital mass.