Classical elements in the magnetoconductance of two-dimensional Lorentz gases

Electrons moving through an array of identically shaped obstacles at random positions form a Lorentz gas. [1] In two-dimensional systems, strong deviations of the magnetoresistance from the Boltzmann model are observed experimentally and in numerical simulations, which have a classical origin. At low magnetic fields, memory effects [2] cause subdiffusive transport, which generates a strong positive magnetoconductivity, while weak localization is absent. At intermediate magnetic fields, the transport develops a superdiffusive character, which is visible as a pronounced maximum in the magnetoconductance at sufficiently large obstacle densities. [3] In dilute two-dimensional Lorentz gases, the interplay between the Lorentz obstacles and the residual background disorder causes strong corrections to the behavior of a clean Lorentz gas.