Hofstadter-type energy spectra in lateral superlattices defined by periodic magnetic and electrostatic fields

TL;DR

This paper investigates the energy spectra of electrons in a two-dimensional lattice influenced by combined periodic magnetic and electrostatic fields, revealing how phase differences affect band structure and Landau levels.

Contribution

It introduces a model combining periodic magnetic and electrostatic modulations with phase control, analyzing their impact on electron energy spectra in 2D lattices.

Findings

Phase differences significantly alter band widths.

Magnetic modulation introduces complex phases affecting Landau levels.

Energy spectra exhibit Hofstadter-type fractal structures.

Abstract

We calculate the energy spectrum of an electron moving in a two-dimensional lattice which is defined by an electric potential and an applied perpendicular magnetic field modulated by a periodic surface magnetization. The spatial direction of this magnetization introduces complex phases into the Fourier coefficients of the magnetic field. We investigate the effect of the relative phases between electric and magnetic modulation on band width and internal structure of the Landau levels.