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 (${\mathrm{\varepsilon }}_{\mathit{F}}$τ${)}^2$ times larger than its average value. We interpret this effect in terms of the diffusive nature of the orbital mass.

• Received 21 December 1989

DOI:https://doi.org/10.1103/PhysRevB.41.10523