Magnetotransport in a nonplanar two-dimensional electron gas

We investigate the magnetoresistance of a nonplanar two-dimensional electron gas (2DEG) fabricated by growth of a GaAs/(AlGa)As heterojunction on a wafer prepatterned with facets at 20° to the substrate. Applying a uniform magnetic field (B) produces a spatially nonuniform component of field perpendicular to the 2DEG. With the field in the plane of the substrate, the resistance measured across an etched facet shows oscillations that are periodic in 1/B. This measurement is equivalent to a two-terminal measurement on a planar Hall bar in a uniform field. Magnetoquantum oscillations are also observed between voltage probes on planar regions of the sample located directly adjacent to the facet where there is no perpendicular field component. These are interpreted as being due to current propagating out from the corners of the facet along the edges of the mesa in a similar fashion to the current in a conventional planar Hall bar, which enters and leaves from diagonally opposite corners. In samples with an even number of facets the symmetry of the magnetoresistance is reversed, consistent with this interpretation.