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 topological chiral superconducting states with Chern number N=1,2,4 (namely p+ip, d+id, g+ig) appear over a large parameter region with mr 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 quasi-particle interference. Moreover, the spin-polarized PDW could lead to spin-polarized superconducting diode effect.