Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

Abstract

In this paper we present calculations on the electronic band structure of a two-dimensional lateral superlattice subject to a perpendicular magnetic field by employing a projection operator technique based on the ray-group of magnetotranslation operators. We construct a new basis of appropriately symmetrized Bloch-like wavefunctions as linear combination of well-localized magnetic-Wannier functions. The magnetic field was consistently included in the Wannier functions defined in terms of free-electron eigenfunctions in the presence of external magnetic field in the symmetric gauge. Using the above basis, we calculate the magnetic energy spectrum of electrons in a lateral superlattice with bi-directional weak electrostatic modulation. Both a square lattice and a triangular one are considered as special cases. Our approach based on group theory handles the cases of integer and rational magnetic fluxes in a uniform way and the provided basis could be convenient for further both analytic and numerical calculations.

Beats of the Magnetocapacitance Oscillations in Lateral Semiconductor Superlattices

“…( 6) are broadened into bands with Van Hove singularities at the edges of each Landau band. On the other hand, if 2D modulation is imposed, the DOS does not exhibit Van Hove singularities reflecting the 2D nature of the electron motion in the Landau bands with finite mean velocities [20].…”