The energy dispersions of the electronic Landau levels in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As lateral-surface superlattices (LSSL’s) with periodically structured interfaces in a normally applied static magnetic field are calculated numerically. The results show that the energy dispersions of the adjacent Landau levels are out of phase, which greatly reduces the energy gaps between the adjacent energy bands and changes the electronic cyclotron frequencies of the LSSL systems. For certain interface structures, the energy gaps will disappear, giving a continuous distribution of the electronic states in the energy space. The effects of the periodically structured interfaces become negligible when the periods of the structured interfaces are much less than the extension, ‖Δx‖=2 √ħc/eB , of the electronic wave functions in magnetic fields. The results also show that the approximation assuming an infinitely high potential barrier between the well GaAs and barrier ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$As is not very accurate in calculating the electronic Landau levels in LSSL’s with periodically structured interfaces. The changes of the energy dispersions of the electronic Landau levels with the magnetic fields and structural parameters of LSSL’s are studied in detail.

• Received 20 October 1992

DOI:https://doi.org/10.1103/PhysRevB.47.7208