# Localization and interactions in topological and non-topological bands in two dimensions

## TL;DR

This paper investigates how disorder, topology, and electron interactions influence localization phenomena in engineered two-dimensional electron systems with tunable topological properties.

## Contribution

It provides a systematic study of single-particle and many-body localization in topological and non-topological subbands derived from Landau levels, highlighting the interplay of disorder, topology, and interactions.

## Key findings

- Disorder affects localization differently depending on the topological nature of the subband.
- Electron-electron interactions can induce or suppress many-body localization in these systems.
- Tuning the band structure allows control over the localization and topological properties of the system.

## Abstract

A two-dimensional electron gas in a high magnetic field displays macroscopically degenerate Landau levels, which can be split into Hofstadter subbands by means of a weak periodic potential. By carefully engineering such a potential, one can precisely tune the number, bandwidths, bandgaps and Chern character of these subbands. This allows a detailed study of the interplay of disorder, interaction and topology in two dimensional systems. We first explore the physics of disorder and single-particle localization in subbands derived from the lowest Landau level, that nevertheless may have a topological nature different from that of the entire lowest Landau level. By projecting the Hamiltonian onto subbands of interest, we systematically explore the localization properties of single-particle eigenstates in the presence of quenched disorder. We then introduce electron-electron interactions and investigate the fate of many-body localization in subbands of varying topological character.