Hall effect in a spatially fluctuating magnetic field with zero mean

We study the Hall effect of a nonplanar stripe-shaped two-dimensional electron gas (2DEG) with stripes oriented perpendicular to the current in the presence of an in-plane external magnetic field B-ext. Since the 2DEG is sensitive only to the normal component of B-ext, the electrons move in a sign alternating magnetic field with zero mean < B > = 0 and nonzero variance, which is proportional to B-ext. A zero Hall resistance is observed at low B-ext, as expected for < B > = 0. However, for B-ext>5 T, a nonzero Hall voltage is found. in this regime the electron transport is characterized by the propagation of chiral snakelike trajectories. These states move in positive and negative directions along stripes and are confined to one-dimensional channels with a different number of propagating modes, which is determined by the surface topography. Asymmetry in the number of ballistic modes leads to a nonzero Hall voltage.