Classical diffusion anomalies in two-dimensional Lorentz gases

The magnetoresistivity of two-dimensional Lorentz gases, formed by a free electron gas exposed to sparse, strong scatterers of identical shape at random positions, shows strong deviations from the Drude-Boltzmann model due to classical memory effects. At intermediate magnetic fields where the cyclotron radius is similar to the obstacle size, a conductance peak is observed which originates from transient superdiffusive motion along, and across, the obstacle clusters. [1] On the other hand, for strongly retroreflective [2] obstacles of sufficiently large number density, transient subdiffusive motion of the electrons is found in molecular dynamics simulations, which increases as the magnetic field approaches zero, and an anomaly ist observed for B=0 where the diffusion constant cannot be defined, similar to earlier kinetic studies at low obstacle densities.[3] A suppression of the longitudinal conductivity around zero magnetic field is measured at sub-Kelvin temperatures and interpreted as an experimental signature of this transport anomaly.

[1] N. H. Siboni et al., Phys. Rev. Lett. 120, 056601 (2018).
[2] J. Schluck et al., Phys. Rev. B 97, 115301 (2018).
[3] E. Hauge and E. Cohen, J. Math. Phys. 10, 397 (1969).