Localized Wavefunctions and Magnetic Band Structure for Lateral Semiconductor Superlattices

TL;DR

This paper develops a group-theoretic approach to calculate the magnetic band structure of lateral semiconductor superlattices, incorporating localized wavefunctions and magnetic effects for different lattice geometries.

Contribution

It introduces a new basis of symmetrized Bloch-like wavefunctions using magnetic Wannier functions for analyzing magnetic band structures in superlattices.

Findings

The method handles integer and rational magnetic fluxes uniformly.

The basis simplifies further analytical and numerical calculations.

Applicable to square and triangular lattice geometries.

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.