BLOCH STATES OF ELECTRONS IN A CORRUGATED QUANTUM CHANNEL IN A MAGNETIC-FIELD

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 band structure at high fields consists of free-electron-like bands associated with magnetic edge states, and flatbands associated with localized Landau levels. 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.