Fractional quantum anomalous Hall effect in a singular flat band

TL;DR

This paper discovers fractional quantum anomalous Hall phases in singular flat bands within twisted bilayer MoTe2, revealing new topological states beyond traditional Landau levels and Chern insulators, with potential cold atom realizations.

Contribution

It demonstrates FQAH phases in singular flat bands, a topologically distinct landscape, and explores how band touching and gapping influence these phases, expanding the understanding of fractional quantum Hall physics.

Findings

FQAH phases found at 1/3 and 2/3 filling in SFB.

Gapping band touching can suppress FQAH effects.

Proposes optical schemes for cold atom realization of SFB.

Abstract

In the search of fractional quantum anomalous Hall (FQAH) effect, the conventional wisdom is to start from a flat Chern band isolated from the rest of the Hilbert space by band gaps, so that many-body interaction can be projected to a landscape that mimics a Landau level. Singular flat bands (SFB), which share protected touching points with other dispersive bands, represent another type of flat landscapes differing from Landau levels and Chern bands in topological and geometric properties. Here we report the finding of FQAH phases in a SFB, which emerges in the bipartite limit of the nearest-neighbor tight-binding model of twisted bilayer MoTe$_2$. At 1/3 and 2/3 filling of the SFB, FQAH effects are demonstrated using density matrix renormalisation group calculations with all bands, as well as exact diagonalization calculations with the two touching bands. Gapping the band touching can turn the SFB into a nearly flat Chern band, but counter-intuitively this suppresses the FQAH effect, as the gap opening introduces strong inhomogeneity to the quantum geometry. An optical scheme to realize such SFB for cold atoms is provided. Our findings uncover a new arena for the exploration of fractional quantum Hall physics beyond the Landau level and Chern insulator paradigms.