Magnetotransport in classical Lorentz gases

Lorentz gases are systems of non-interacting, free particles that move in an array of identical obstacles at random positions. The magnetoresistance of two-dimensional Lorentz gases in the classical regime deviates markedly from the predictions of the Drude-Boltzmann model. This can be traced back to memory effects, which have their origin in the static character of the scattering potential landscape. Examples are electrons completing the cyclotron orbit without getting scattered, experiencing several successive bounces at the same obstacle or getting retroreflected into a region free of scatterers. As a consequence, the Lorentz gas has a nontrivial phase diagram, composed of two insulating phases that are separated by one conductive phase.

In this presentation, we will show that memory effects generate characteristic textures in the magnetotransport. While an exponentially decaying component  can be attributed to the closed cyclotron motion, we observe a linear magnetoresistance at small magnetic fields which originates from retroreflection. Most strikingly, a pronounced magnetoconductance maximum is observed at intermediate magnetic fields which is interpreted as a residue of the two phase transitions that cannot be directly observed. Numerical simulations show that the electronic motion  close to this peak has a non-Gaussian statistics and rather resembles Lévy flights.