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

Abstract

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 \ensuremath{\nabla}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 \ensuremath{\Vert}B\ensuremath{\Vert} is minimum. In the opposite direction, the Landau states propagate throughout the rest of the sample with a velocity proportional to \ensuremath{\Vert}\ensuremath{\nabla}B${\mathrm{\ensuremath{\Vert}}}^{1/2}$.