Current distributions and the de Haas-van Alphen oscillation in a planar system of Hall electrons

TL;DR

This paper investigates the current distribution in a finite two-dimensional Hall electron system, highlighting how edge and Hall currents differ and relate to quantum effects like de Haas-van Alphen oscillations.

Contribution

It provides a detailed analysis of equilibrium edge and Hall current distributions, revealing their dependence on electron edge states and their distinct behaviors.

Findings

Edge current distribution changes with electron edge states.

Edge current exhibits de Haas-van Alphen oscillations.

Fast electrons along edges are not primary Hall current carriers.

Abstract

The current distribution is studied for a finite-width two-dimensional system of Hall electrons, with a clear distinction drawn between the equilibrium edge current and the Hall current. It is pointed out that both the distribution and direction of the equilibrium edge current change dramatically as the number of electron edge states increases, and that this alternating edge current is another manifestation of the de Haas-van Alphen effect. The Hall-current distribution is substantially different from the edge current distribution, and it is shown numerically that the fast-traveling electrons along the sample edge are not the main carriers of the Hall current.