  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
new 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.
