Quantum criticality and superconductivity in twisted transition metal dichalcogenides

We analyze a model for electronic structure and interactions in twisted transition metal chalcogenide WSe2 for superconductivity. In this material, spin-orbit scattering locks the z components of spins of low-energy fermions near the K and K′ corner points of the hexagonal Brillouin zone, reducing the symmetry of spin-spin interactions to that of an XY model. We show that a nominally repulsive 4-fermion interaction gives rise to an attraction for pairing in a two-component E- channel, which is a hexagonal lattice representation of ℓ=1 channels. The gap function is inversion-odd and a linear combination of spin singlet and spin triplet. At weak coupling, superconductivity emerges via the Kohn-Luttinger mechanism; we compute Tc for the Fermi-level lying close to the van Hove singularity. At strong coupling, the pairing is mediated by XY magnetic fluctuations peaked at momenta K-K′=2K and we estimate Tc using the form of the quantum-critical XY fluctuations, displaying ω/T scaling.