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

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.

7 pages, 8 figures

References in corpus (8)

• Electrically tunable transverse magnetic focusing in graphene
• Transverse Electron Focusing in Systems with Spin-Orbit Coupling
• Influence of dephasing process on the quantum Hall effect and the spin Hall effect
• How branching can change the conductance of ballistic semiconductor devices
• Magnetic breakdown of cyclotron orbits in systems with Rashba and Dresselhaus spin-orbit coupling
• Andreev drag effect via magnetic quasiparticle focusing in normal-superconductor nanojunctions
• Magnetic focusing in normal-superconductor hybrid systems: a semiclassical analysis
• Statistical model for the effects of phase and momentum randomization on electron transport

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• Edge magnetotransport in graphene: A combined analytical and numerical study
• Understanding magnetic focusing in graphene $p$-$n$ junctions through quantum modeling
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• Nonequilibrium distribution functions in electron transport: Decoherence, energy redistribution and dissipation
• Breathing mode in open-orbit magnetotransport: a magnetic lens with a quantum mechanical focal length
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