MAGNETIC EDGE STATES IN A CORRUGATED QUANTUM CHANNEL

We calculate the band structure of a long ballistic channel whose width is modulated periodically in the presence of a perpendicular magnetic field. The channel is narrowed on one side only, the other wall remaining straight. At zero magnetic field, the periodic modulation of the width produces miniband gaps. As the magnetic field is increased, the gaps disappear. The vanishing of the miniband gaps is related to the suppression of backscattering in edge-state transport discussed by Buttiker [M. Buttiker, Phys. Rev. B 38, 9375 (1988)]. The band structure at high fields consists of free-electron-like bands associated with magnetic edge states, and flat bands associated with localized Landau levels. We calculate the wave functions and current densities associated with these states. The asymmetry in the walls causes electrons moving through the channel in one direction to have a different effective mass from electrons moving in the opposite direction.