Band structure and band topology in twisted homotrilayer transition metal dichalcogenides

We investigate an idealized continuum model of a twisted homotrilayer transition metal dichalcogenides with negligible next-nearest-layer couplings. We systematically analyze band structure and topology of various stacking configurations in a twist angle range from ${1}^{\ensuremath{\circ}}$ to ${4}^{\ensuremath{\circ}}$. This allows us to uncover a plethora of topological transitions as well as various angle regimes with flat bands, some of them topologically nontrivial, which are of growing interest for the realization of exotic strongly correlated phases. Additionally, we uncover surprising properties, such as that for certain stacking configurations, some layers effectively decouple from other layers. In this case, the only remnant of coupling between layers is a layer-dependent energy shift.