Higher Chern bands in helically twisted transition metal dichalcogenide homotrilayers

We propose helically twisted transition metal dichalcogenide homotrilayers as a platform for realizing correlated topological phases of matter with higher and tunable Chern numbers. For small twist angles, we find that a clear separation of the moiré and supermoiré length scales allows us to construct a low-energy continuum model describing the physics of moiré-scale domains characterized by a high-symmetry stacking configuration. We identify regimes of twist angle and displacement field strength where the topmost valence band is both isolated and topological with a K-valley Chern number of C = -2. We show that tuning the displacement field can cause a transition from a C = -2 to a C = -1 band, as well as a transition from a topologically trivial band to one with C = -1. We further construct an effective tight-binding model for a high-symmetry stacking domain that is valid over a wide range of twist angles, and also show that the C = -2 band can remain stable at filling fraction ν = -1 in the presence of Hartree-Fock–level interactions.