Higher Chern bands in helical homotrilayer transition metal dichalcogenides

We propose helically twisted homotrilayer transition metal dichalcogenides as a platform for realizing correlated topological phases of matter with higher and tunable Chern numbers. We show that a clear separation of scales emerges for small twist angles, allowing us to derive a low-energy continuum model that captures the physics within moir\'e-scale domains. We identify regimes of twist angle and displacement field for which the highest-lying hole band is isolated from other bands and is topological with $K$-valley Chern number $C=-2$. We demonstrate that varying the displacement field can induce a transition from $C=-2$ to $C=-1$, as well as from a topologically trivial band to a $C=-1$ band. We derive an effective tight-binding description for a high-symmetry stacking domain which is valid for a wide range of twist angles, and we show that the $C=-2$ band can remain stable at filling fraction $\nu=-1$ in the presence of interactions in Hartree-Fock calculations.