Topological Wigner-Mott Insulators in Fractionally-Filled Topological Bands

The recent emergence of highly-tunable correlated states in van der Waals heterostructures has caused great interest in the interplay of band topology and strong electronic interactions. While ordinary mechanisms for forming Mott insulators rely on strong Coulomb repulsion to localize electrons, Wannier obstructions in half-filled topological bands preclude this kind of localization. Here, we show that at fractional commensurate fillings, a loophole follows from the spontaneous breaking of translation symmetry. We introduce Topological Supercell Wannier functions (TSWFs), which naturally segregate a fractionally-filled topological band into two parts in the folded Brillouin zone: Tightly-localized orbitals, and itinerant delocalized states that retain the topological obstruction. Strong Coulomb interactions preferentially trap local moments in the localized orbitals, forming a hierarchy of topological Wigner-Mott insulators with emergent magnetic order at low temperatures. We demonstrate that their stability can be understood from quantum-geometric bounds for TSWFs, and describe possible experimental signatures in moiré heterostructures at fractional filling.