Weak localization in transition metal dichalcogenide monolayers and their heterostructures with graphene

We calculate the interference correction to the conductivity of doped transition metal dichalcogenide (TMDC) monolayers. Because of the interplay between valley structure and intrinsic spin-orbit coupling (SOC), these materials exhibit a rich weak localization (WL) behavior that is qualitatively different from conventional metals or similar two-dimensional materials such as graphene. Our results can also be used to describe graphene/TMDC heterostructures, where the SOC is induced in the graphene sheet. We discuss parameter regimes that go beyond existing theories, and can be used to interpret recent experiments in order to assess the strength of SOC and disorder. Furthermore, we show that an in-plane Zeeman field can be used to distinguish the contributions of different kinds of SOC to the WL magnetoconductance.