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

Interplay between snake and quantum edge states in a graphene Hall bar with a pn-junction

“…Similar interference effect was found recently in Ref. 18 for edge channels in the case of transverse electron focusing of a normal 2D electron gas at the GaAs-AlGaAs interface. meV the carriers are depleted under the gate.…”

Edge magnetotransport in graphene: A combined analytical and numerical study

“…However, in graphene the linear dispersion, the valley degeneracy (symmetry points K and K in momentum space) as well as the nontrivial edge geometry add subtle but important new aspects. In this way, at first sight the local current flow looks similar in both systems (cyclotron orbits, edge channels), compare figure 5 with figure 2 in [28]. However, the boundary geometry has a distinct effect on the local current flow, see figure 6, which will be discussed in section 4.5.…”

“…Although the charge carriers in graphene behave as relativistic massless fermions, the studied stripes show properties similar to a nonrelativistic 2DEG [28]: Classical focusing peaks in weak magnetic fields, followed by anomalous resistance oscillations when the magnetic field strength is increased. In both systems the resistance oscillations can be explained by the interference of the plane wave part of the occupied edge states.…”

Current flow paths in deformed graphene: from quantum transport to classical trajectories in curved space

“…self-energy by means of which we introduce absorbing boundaries[55], mimicking infinite dimensions of the graphene sheet. (The sum runs over the edge atoms C, see green sites in figure 2, and h > 0 is a constant.)…”