Chiral two-dimensional electron gas in a periodic magnetic field

TL;DR

This paper investigates how a periodic magnetic field influences the energy bands and topological properties of a two-dimensional electron gas, revealing tunable localization, persistent currents, and quantized Hall conductivity.

Contribution

It demonstrates the continuous transformation of electron states from free to localized and analyzes the topological Chern numbers in a periodic magnetic field with a triangular lattice.

Findings

Electron energy bands can be tuned by magnetic field strength.

Localized chiral electron states lead to persistent currents.

Hall conductivity becomes quantized when Fermi level is in a gap.

Abstract

We study the energy spectrum and electronic properties of two-dimensional electron gas in a periodic magnetic field of zero average with a symmetry of triangular lattice. We demonstrate how the structure of electron energy bands can be changed with the variation of the field strength, so that we can start from nearly free electron gas and then transform it continuously to a system of essentially localized chiral electron states. We find that the electrons near some minima of the effective potential are responsible for occurrence of dissipationless persistent currents creating a lattice of current contours. The topological properties of the electron energy bands are also varied with the intensity of periodic field. We calculated the topological Chern numbers of several lower energy bands as a function of the field. The corresponding Hall conductivity is nonzero and, when the Fermi level lies in the gap, it is quantized.