Singlet, triplet, and pair density wave superconductivity in the doped triangular-lattice moir system

Recent experimental progress has established the twisted bilayer transition metal dichalcogenide (TMD) as a highly tunable platform for studying many-body physics. Particularly, the homobilayer TMDs under displacement field are believed to be described by a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase theta. To explore the effects of theta on the system, we perform density matrix renormalization group calculations for the relevant triangular lattice t-J model. By changing theta at small hole doping, we obtain a region of quasi-long-range superconducting order coexisting with charge and spin density wave within 0 < theta < pi /3. The superconductivity is composed of a dominant spin singlet d-wave and a subdominant triplet p-wave pairing. Intriguingly, the S-z = +/- 1 triplet pairing components feature pair-density waves. In addition, we find a region of triplet superconductivity coexisting with charge-density wave and ferromagnetism within pi /3 < theta < 2 pi /3, which is related to the former phase at smaller theta by a combined operation of spin-flip and gauge transformation. Our findings provide insights and directions for experimental search for exotic superconductivity in twisted TMD systems.