Theory of Topological Superconductivity and Antiferromagnetic Correlated Insulators in Twisted Bilayer WSe${}_2$

Since the very recent discovery of unconventional superconductivity in twisted WSe${}_2$ homobilayers at filling $\nu =-1$, considerable interest has arisen in revealing its mechanism. In this paper, we developed a three-band tight-binding model with non-trivial band topology by direct Wannierization of the low-energy continuum model. Incorporating both onsite Hubbard repulsion and next-nearest-neighbor attraction, we then performed a mean-field analysis of the microscopic model and obtained a phase diagram qualitatively consistent with the experiment results. For zero or weak displacement field, the ground state is a Chern number $C=\pm 2$ topological superconductor in the Altland-Zirnbauer A-class (breaking time-reversal but preserving total $S_z$ symmetry) with inter-valley pairing dominant in $d_{xy}\pm i{d}_{x^2-y^2}$-wave (mixing with a subdominant $p_x\mp i{p}_y$-wave) component. For a relatively strong displacement field, the ground state is a correlated insulator with the ${120}^{\circ }$ antiferromagnetic order. Our results provide new insights into the nature of the twisted WSe${}_2$ systems and suggest the need for further theoretical and experimental explorations.