Magnetotransport along a boundary: From coherent electron focusing to edge channel transport

TL;DR

This paper theoretically investigates electron focusing and edge channel transport in a 2D electron system under magnetic fields, revealing classical, quantum Hall, and novel interference oscillations in Hall resistance.

Contribution

It introduces a comprehensive Green's function approach to analyze boundary electron transport, uncovering new interference effects between edge channels.

Findings

Equidistant peaks in Hall resistance at weak fields

Quantum Hall plateau at strong fields

Novel interference oscillations in intermediate fields

Abstract

We study theoretically how electrons, coherently injected at one point on the boundary of a two-dimensional electron system, are focused by a perpendicular magnetic field $B$ onto another point on the boundary. Using the non-equilibrium Green's function approach, we calculate the generalized 4-point Hall resistance $R_{xy}$ as a function of B. In weak fields, $R_{xy}$ shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, $R_{xy}$ shows a single extended plateau reflecting the quantum Hall effect. In intermediate fields, we find superimposed upon the lower Hall plateaus anomalous oscillations, which are neither periodic in 1/B (quantum Hall effect) nor in $B$ (classical cyclotron motion). The oscillations are explained by the interference between the occupied edge channels, which causes beatings in $R_{xy}$. In the case of two occupied edge channels, these beatings constitute a new commensurability between the magnetic flux enclosed within the edge channels and the flux quantum. Introducing decoherence and a partially specular boundary shows that this new effect is quite robust.