Wigner-Mott states in fractionally filled topological moiré bands

Twisted transition metal dichalcogenide (TMD) heterostructures are a highly-tunable platform for realizing many-body correlated states. In particular, they allow studying the interplay between band topology and strong electronic correlations in experimentally realizable systems. Here, we show that in addition to conventional fractional quantum Hall states, topological bands in twisted TMDs can host a topological Mott insulator with broken translation symmetry and zero net magnetization at fractional commensurate fillings. In a topological band, a Mott-like picture of charges forming local moments is in apparent conflict with the inability to form exponentially localized Wannier functions. We have developed a loophole that leverages translation symmetry breaking to exponentially localize a subset of charge degrees of freedom, providing a concise heuristic to understand the stability of Mott insulators at fractional filling in the presence of topological obstructions. We use this construction to explain the possibility for a topological Mott insulator in twisted MoTe2, and study its competing magnetic orders using exact diagonalization. Potential applications to recently observed correlated insulating states in moiré systems are also discussed.