Superconductivity in the Triangular-Lattice t-J Model of Twisted Bilayer Transition Metal Dichalcogenide

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 TMD is believed to be a quantum simulator of a generalized triangular-lattice Hubbard model with a spin-dependent hopping phase θ that is induced by a displacement field. To explore the effects of θ on the system state, we perform density matrix renormalization group calculation of the relevant triangular lattice t-J model on a four-leg cylinder. By changing θ for lightly doped systems, we identify different quantum phases: a stripe charge density wave phase (CDW), a superconducting phase without charge stripes (SC) and a

superconducting phase coexisting with charge stripes (SC+CDW). The SC and SC+CDW phases are found to host a mixture of spin singlet and triplet pairing, and the pairing correlations decay in a power-law fashion with exponent smaller than two. Additionally, we discuss important effects of the flux through the center of finite cylinders. Our findings could be a useful guide for experimental search for superconductivity in twisted TMD systems.