Magneto-Transport in the Two-Dimensional Lorentz Gas

TL;DR

This paper investigates the magneto-transport properties of a two-dimensional Lorentz gas with randomly distributed scatterers under a perpendicular magnetic field, analyzing conductance and correlation behaviors across different regimes.

Contribution

It provides numerical analysis of velocity autocorrelation and conductance in the Lorentz gas, comparing results with theoretical models and exploring effects of magnetic fields and density.

Findings

Long time tail persists at $t^{-2}$ for non-zero magnetic fields.

Conductance results align with mode-coupling theory at low densities.

Percolation threshold influences transition between hopping and edge current transport.

Abstract

We consider the two-dimensional Lorentz gas with Poisson distributed hard disk scatterers and a constant magnetic field perpendicular to the plane of motion. The velocity autocorrelation is computed numerically over the full range of densities and magnetic fields with particular attention to the percolation threshold between hopping transport and pure edge currents. The Ohmic and Hall conductance are compared with mode-coupling theory and a recent generalized kinetic equation valid for low densities and small fields. We argue that the long time tail as $t^{-2}$ persists for non-zero magnetic field.