Effect of a fluctuating magnetic field on weak localization in a two-dimensional disordered system

We consider a charged quantum particle in a two-dimensional disordered system subject to a spatially and temporally fluctuating magnetic field. The fluctuations are assumed to be Gaussian, with correlations typical for a metal in the anomalous-skin-effect regime. We derive a scaling form for the quantum correction to the conductivity in terms of a scaled temperature, elastic mean free path, and magnetic field. The weak localization correction to the conductivity is calculated for the case of rapid magnetic-field fluctuations. We express the result in terms of a phenomenological phase relaxation rate 1/${\mathrm{\tau }}_{\mathrm{\phi }}^{\mathrm{*}}$, which is found to scale with temperature as ${\mathit{T}}^{1/3}$, provided the potential disorder is sufficiently strong and the temperature is above a critical value. In all other cases, including the normal-skin-effect regime and the case of quasistatic field fluctuations, 1/${\mathrm{\tau }}_{\mathrm{\phi }}$ is found to be proportional to T, albeit with unusual prefactors.