Duality Relation among Periodic Potential Problems in the Lowest Landau Level

TL;DR

This paper explores the duality between potential period and magnetic length in 2D electron systems under magnetic fields, revealing spectra with Hofstadter and flat bands, and linking potential problems to tight-binding models.

Contribution

It introduces a duality relation in the energy spectra of periodic potential problems in the lowest Landau level, connecting potential period and magnetic length.

Findings

Spectra exhibit Hofstadter-type and flat bands.

Energy spectra satisfy a duality relation between potential period and magnetic length.

Connection established between potential problems and tight-binding models.

Abstract

Using a momentum representation of a magnetic von Neumann lattice, we study a two-dimensional electron in a uniform magnetic field and obtain one-particle spectra of various periodic short-range potential problems in the lowest Landau level.We find that the energy spectra satisfy a duality relation between a period of the potential and a magnetic length. The energy spectra consist of the Hofstadter-type bands and flat bands. We also study the connection between a periodic short-range potential problem and a tight-binding model.