Fractional quantum anomalous Hall effect in a singular flat band, part I

In the search for fractional quantum anomalous Hall (FQAH) effect, the conventional wisdom is to construct a flat Chern band well isolated in the energy spectrum, so that Coulomb interaction can be projected onto a single band that mimics a Landau level. Singular flat bands (SFB), which share protected touching points with other dispersive bands, represent another class of flat-band landscape differing from Landau levels and Chern bands in quantum geometric properties. Interestingly, in this work [1] we find FQAH phases in an SFB, whose model corresponds to the nearest-neighbor tight-binding description of twisted bilayer MoTe₂ in the bipartite limit. At 1/3 and 2/3 filling of the SFB, the FQAH effects are confirmed by density matrix renormalization group and exact diagonalization calculations that consider the effects of band mixing. Breaking the band touching can turn the SFB into an isolated and nearly flat Chern band, but counter-intuitively, the FQAH effects are suppressed, which can be attributed to the increased inhomogeneity in the quantum geometry accompanying the gap opening. An optical scheme to realize such an SFB with cold atoms is proposed. Our results showcase a new playground for exploring the fractional quantum Hall physics beyond the Landau level and Chern insulator paradigms.