Hall effect in a two-dimensional disordered Lorentz gas

Using a combination of experiment and simulation, we study the magnetotransport in a two-dimensional disordered Lorentz gas with circular obstacles. Our focus is on the investigation of the Hall effect at obstacle densities beyond the low-density limit. However, as a reference, we also consider very low obstacle densities. Here, the magnetotransport properties, as obtained from the simulation and the experiment of a pristine sample, can be well described in terms of the Drude-Boltzmann model. For intermediate and high obstacle density, only for very low magnetic fields B, we find a linear dependence of the Hall resistance xy on B, albeit with a Hall coefficient that does not reflect properly the carrier density. At larger magnetic fields but still below the onset of the Landau quantization as well as the magnetic-field-induced conductor-to-insulator transition, striking nonlinearities of xy(B) due to classical memory effects are observed. Moreover, the scattering time obtained within the Drude-Boltzmann model develops into a phenomenological parameter that decreases with increasing magnetic field.