Pair-Density-Wave and Chiral Superconductivity in Twisted Bilayer Transition Metal Dichalcogenides

We theoretically explore possible orders induced by weak repulsive interactions in twisted bilayer transition metal dichalcogenides (e.g., WSe2) in the presence of an out-of-plane electric field. Using renormalization group analysis, we show that superconductivity survives even with the conventional van Hove singularities. We find that topological chiral superconducting states with Chern number N = 1, 2, 4 (namely, p + ip, d + id, and g + ig) appear over a large parameter region with a moire ' filling factor around n = 1. At some special values of applied electric field and in the presence of a weak out-of-plane Zeeman field, spin-polarized pair-density-wave (PDW) superconductivity can emerge. This spin-polarized PDW state can be probed by experiments such as spin-polarized STM measuring spin-resolved pairing gap and quasiparticle interference. Moreover, the spin-polarized PDW could lead to a spin-polarized super-conducting diode effect.