Electron transport through one-dimensional lateral surface superlattices in magnetic fields

A scattering-matrix method for the calculations of electron transport through lateral quantum systems in the presence of a perpendicular magnetic field is developed and is used to investigate the effects of an applied magnetic field on electron transport through a quantum channel modulated by a smooth periodic potential along the direction of the current flow. At zero magnetic field, the calculated conductance displays regular dips due to the formation of minigaps (or the Bragg reflections) and the rapid oscillations due to electron transmission through the coupled quasi-zero-dimensional states in the cavity regions between the potential barriers. Both are shown to be suppressed when a magnetic field is applied to the quantum channel. This is interpreted as the formation of propagating edge states. However, other irregular dips are shown to appear in the conductance of the modulated channel in the presence of the magnetic field. These dips reflect the coupling between the electron states propagating along the opposite edges of the channel and may appear so densely in a wide quantum channel with a strong modulation that the conductance exhibits fluctuations. In the high-field regime where the magnetic length ${\mathit{l}}_{\mathit{B}}$ is much smaller than the channel width w, these irregular dips are seen to be also suppressed, leading to a nearly perfect recovery of the conductance quantization.