Magnetoresistance due to classical memory effects in a three-dimensional electron gas

Magnetoresistance (MR) provides a powerful tool for probing the non-Markovian nature of transport in a magnetic field. Long-range disorder gives rise to a nontrivial MR due to classical memory effects, arising from multiple returns to the same position. While the presence of such disorder has been indicated in various materials, there have been few rigorous studies on these effects in 3D systems. In this talk, I will discuss the results of our analysis of the transverse (TMR), as well as longitudinal MR (LMR) of a 3D electron gas, due to a long-range a) random magnetic field and b) random potential, within a semiclassical Boltzmann approach, with and without short-range disorder. To account for non-Markovian processes, the disorder is incorporated as a random force on the LHS of the Boltzmann equation, analogous to previous studies in 2D. We perform a perturbative expansion for the Green's function of the Boltzmann equation, and thus for the conductivity, in the correlation function of the long-range disorder. In the absence of short-range disorder, the unperturbed Green's function is singular due to a zero mode, and the field-dependence of the conductivity is estimated by resumming the perturbation series to all orders. From our analysis, we obtain a prominent TMR as well as LMR, which generally peak or saturate at a characteristic field scale where the correlation length becomes comparable to the cyclotron radius.