Magnetoresistance due to classical memory effects in three-dimensional conductors

Magnetoresistance (MR) provides a powerful tool for probing the
non-Markovian nature of transport in a magnetic field. In the
semiclassical limit, sufficiently long-range disorder can give rise to a
nontrivial magnetoresistance due to classical memory effects, associated
with multiple returns of electron trajectories between scattering events.
Such non-Markovian effects can be taken into account within the
semiclassical Boltzmann equation, provided the disorder is treated as a
random force term in the Liouville operator. While the presence of such
disorder has been indicated in different materials, there have been few
rigorous studies on these effects in 3D systems. In this talk, I will be
discussing our recent results for the semiclassical magnetoresistivity due
to a weak, long-range a) random magnetic field (RMF), b) random potential
(RP) in a 3D electron gas at classically strong fields. For our analysis,
we write down a perturbative expansion for the Green’s function of the
modified Liouville operator, and therefore for the conductivity, in the
correlation function of long-range disorder. In the absence of short-range
disorder, the Green’s function is found to be singular due to a zero mode,
and the field-dependence of the conductivity is obtained by re-summing the
perturbation series to all orders. We find a significant transverse
magnetoresistance, which either peaks or saturates at a characteristic
field scale where the correlation length of the disorder becomes
comparable to the cyclotron radius.