Electron Band Structure in a Two Dimensional Periodic Magnetic Field

TL;DR

This paper explores the energy spectrum of a 2D electron gas in various periodic magnetic fields, revealing bandwidth oscillations and linking magnetic structures to electronic properties, with potential applications in superconductor heterostructures.

Contribution

It provides a comprehensive analysis of the band structure in 2DEG under arbitrary shaped periodic magnetic fields, including conditions relating magnetic and electric modulations.

Findings

Bandwidth oscillation as a function of Landau index

Relation between vortex lattice structure and energy spectrum

Conditions for equivalence of magnetic and electric modulations

Abstract

In this paper we study the energy spectrum of a two dimensional electron gas (2DEG) in a two dimensional periodic magnetic field. Both a square magnetic lattice and a triangular one are considered. We consider the general case where the magnetic field in a cell can be of any shape. A general feature of the band structure is bandwidth oscillation as a function of the Landau index. A triangular magnetic lattice on a 2DEG can be realized by the vortex lattice of a superconductor film coated on top of a heterojunction. Our calculation indicates a way of relating the energy spectrum of the 2DEG to the vortex structure. We have also derived conditions under which the effects of a weak magnetic modulation, periodic or not, may be reproduced by an electric potential modulation, and vice versa.