  Recent experiments have observed correlated insulating and possible
superconducting phases in twisted homobilayer transition metal dichalcogenides
(TMDs). Besides the spin-valley locked moire bands due to the intrinsic Ising
spin-orbit coupling, homobilayer moire TMDs also possess either logarithmic or
power-law divergent Van Hove singularities (VHS) near the Fermi surface,
controllable by an external displacement field. The former and the latter are
dubbed conventional and higher-order VHS, respectively. Here, we perform a
perturbative renormalization group (RG) analysis to unbiasedly study the
dominant instabilities in homobilayer TMDs for both the conventional and
higher-order VHS cases. We find that the spin-valley locking largely alters the
RG flows and leads to instabilities unexpected in the corresponding
extensively-studied graphene-based moire systems, such as spin- and
valley-polarized ferromagnetism and topological superconductivity with mixed
parity. In particular, for the case with two higher-order VHS, we find a
spin-valley-locking-driven metallic state with no symmetry breaking in the TMDs
despite the diverging bare susceptibility. Our results show how the spin-valley
locking significantly affects the RG analysis and demonstrate that moire TMDs
are suitable platforms to realize various interaction-induced spin-valley
locked phases, highlighting physics fundamentally different from the
well-studied graphene-based moire systems.
