Effects of screening on the Hofstadter butterfly

TL;DR

This paper investigates how electron-electron interactions and screening influence the energy spectrum of a 2D electron gas in a magnetic field with a superlattice, revealing oscillations in Landau band bandwidths and conditions for miniband resolution.

Contribution

It provides a theoretical analysis of screening effects on the Hofstadter butterfly spectrum within the Hartree approximation, highlighting the impact of interactions on band structure.

Findings

Landau band bandwidth oscillates with filling due to screening

Miniband structure becomes resolvable under certain conditions

Strong modulation enhances miniband visibility

Abstract

We study, within the Hartree approximation, the effects of the electron-electron interaction on the energy spectrum of a two-dimensional electron gas in a perpendicular homogeneous magnetic field and a lateral superlattice potential with square symmetry. Due to the strong screening effects, the bandwidth of the Landau bands oscillates strongly with their filling. For short enough periods and strong enough modulation of the superlattice potential, the miniband structure of the Landau bands can be resolved in the thermodynamic density of states.