Memorization of short-range potential fluctuations in Landau levels

TL;DR

This paper investigates how a two-dimensional electron system in a magnetic field can retain memory of short-range potential fluctuations due to Coulomb interactions, showing hysteresis and stability in energy spectra.

Contribution

It introduces a self-consistent numerical approach revealing hysteresis-like behavior and potential memory effects in electron energy spectra under periodic potentials.

Findings

Energy spectra exhibit hysteresis-like properties.

Electron density remains stable after external potential is removed.

System can memorize short-range potential fluctuations.

Abstract

We calculate energy spectra of a two-dimensional electron system in a perpendicular magnetic field and periodic potentials of short periods. The Coulomb interaction is included within a screened Hartree-Fock approximation. The electrostatic screening is poor and the exchange interaction amplifies the energy dispersion. We obtain, by numerical iterations, self-consistent solutions that have a hysteresis-like property. With increasing amplitude of the external potential the energy dispersion and the electron density become periodic, and they remain stable when the external potential is reduced to zero. We explain this property in physical terms and speculate that a real system could memorize short-range potential fluctuations after the potential has been turned off.