Giant Hall effect in the ballistic transport of two-dimensional electrons

TL;DR

This paper investigates the ballistic transport of two-dimensional electrons in a Hall sample, revealing that asymmetric boundary conditions can significantly enhance the Hall coefficient in low magnetic fields.

Contribution

It introduces the analysis of asymmetric boundary reflections in ballistic 2D electron transport, showing a parametric increase in the Hall coefficient compared to symmetric cases.

Findings

Hall coefficient becomes parametrically large in asymmetric samples.

Edge scattering dominates transport when bulk scattering is negligible.

Asymmetry in boundary reflections significantly affects magnetotransport properties.

Abstract

We have studied magnetotransport of a degenerate two-dimensional electron gas in a Hall sample in the Knudsen regime, when the mean free paths of electrons with respect to their collisions with each other and with impurities are much larger than the width of the sample. In contrast to the usually considered symmetric sample, whose both its edges reflect electrons diffusely, we considered an asymmetric sample, one edge of which reflects them diffusely, while the other specularly. It is shown that in such structure in low magnetic fields the Hall coefficient is parametrically large in comparison with its standard value. Also the situation is discussed when all types of scattering can be neglected except for scattering at the edges of the sample.