Electron localization in two-dimensional topological and non-topological bands

Many-body localization (MBL) is a well-established phase present in disordered one-dimensional spin models with short-range interaction. However, the stability of MBL in higher dimensions, in the presence of long range interaction and under the effect of a topologically non-trivial single-particle band structure, is still an area of ongoing research. We demonstrate a method to construct nearly flat subbands with arbitrary Chern numbers, using a weak periodic potential in the lowest Landau level. This two-dimensional system is a novel platform for the detailed study of the interplay between disorder, interaction and topology in a continuum model. Using exact diagonalization, we investigate the localization properties of single-particle eigenstates, as well as the tendency to many-body localize in the presence of interaction, both in the quasi 1-D and 2-D limits. Our results are based on an analysis of both the many-body eigenvalue spacings and the time evolution of an initial charge imbalance [1], [2].

[1] A. Krishna, M. Ippoliti, and R. N. Bhatt, Phys. Rev. B 99, 041111(R) (2019)
[2] A. Krishna, M. Ippoliti, and R. N. Bhatt, Phys. Rev. B 100, 054202 (2019)