Effect of a nonuniform magnetic field on a two-dimensional electron gas in the ballistic regime

The single-particle electronic structure of a two-dimensional electron gas in a nonuniform magnetic field B consists of states that propagate perpendicularly to the field gradient ∇B and have a remarkable time-reversal asymmetry. In one of the allowed directions the propagation has free-electron character and is confined to a narrow one-dimensional channel localized about the region where ‖B‖ is minimum. In the opposite direction, the Landau states propagate throughout the rest of the sample with a velocity proportional to ‖∇B${\mathrm{\Vert }}^{1/2}$.