Tunable topological states with and without flat bands in semiconductor heterostructures*

Moiré heterostructures based on transition metal dichalcogenide bilayers have emerged in recent years as a new platform for strongly interacting physics in which strongly correlated and topologically non-trivial phases of matter have already been observed experimentally. 

We discuss two mechanisms by which topology, the quantum anomalous Hall (QAH) effect, can emerge in these systems. 

First, QAH can arise in TMD homobilayers at small relative twist angles due to interaction effects in the presence of flat topological bands.  In [arXiv:2106.11954], we derive a "magic angle" condition for twisted TMD homobilayers (similar to in bilayer graphene), at which the first moire bands are almost exactly flat, well separated from other bands, and topological.  

Second, we present a new mechanism by which topology can emerge even without flat bands [arXiv:2109.13909].  Our theory explains the recent experimental observation of a QAH state in AB-stacked MoTe₂/WSe₂ tuned by displacement field [arXiv:2107.01796].  Our mechanism shows that QAH can emerge quite generically in these systems.  We predict that the QAH state is a mostly intervalley-coherent state, with only a small valley polarization.