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arXiv · 1302.6178

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

Thomas Stegmann·Dietrich E. Wolf·Axel Lorke
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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.

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Thomas Stegmann, Dietrich E. Wolf, Axel Lorke. 2013-11-27. Magnetotransport along a boundary: From coherent electron focusing to edge channel transport. https://doi.org/10.1088/1367-2630%2F15%2F11%2F113047

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