Studies of Localization in a Fraction of the Lowest Landau Level

The problem of localization in the lowest Landau level has been studied extensively and is known to exhibit a diverging localization length due to the presence of topological extended states. In the presence of interactions, these states were shown to delocalize the entire spectrum [1]. We consider the case of a disordered two-dimensional electron system in a high magnetic field with a periodic delta-function potential, which splits the lowest Landau level into Hofstadter subbands. Our particular choice of potential allows us to isolate a set of subbands with vanishing total Chern number and with tunable bandwidth-to-bandgap ratio. By projecting the system into one such set of bands, we are able to investigate the nature of localization in a topologically trivial fraction of the lowest Landau level. We study the projected problem by numerical exact diagonalization and compare the results to those obtained without the projection procedure, thus shedding light on the role of topological extended states in hindering localization. The stability of the localized phase to interactions and the possibility of a many-body localized regime is also studied.
[1] S. D. Geraedts and R. N. Bhatt, Phys. Rev. B 95, 054303 (2017)