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

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 four-point Hall resistance Rxy as a function of B. In weak fields, Rxy shows the characteristic equidistant peaks observed in the experiment and explained by classical cyclotron motion along the boundary. In strong fields, Rxy 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 Rxy. 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.