Theory of intervalley-coherent AFM order and topological superconductivity in tWSe$_2$

Abstract: The recent observation of superconductivity in the vicinity of insulating or Fermi surface reconstructed metallic states has established twisted bilayers of WSe$_2$ as an exciting platform to study the interplay of strong electron-electron interactions, broken symmetries and topology. In this work, we study the emergence of electronic ordering in twisted WSe$_2$ driven by gate-screened Coulomb interactions. Our first-principles treatment begins by constructing moir\'e Wannier orbitals that faithfully capture the bandstructure and topology of the system and project the gate-screened Coulomb interaction onto them. Using unbiased functional renormalization group calculations, we find an interplay between intervalley-coherent antiferromagnetic order and chiral, mixed-parity $d/p$-wave superconductivity for carrier concentrations near the displacement field-tunable van-Hove singularity. Our microscopic approach establishes incommensurate intervalley-coherent antiferromagnetic spin fluctuations as the dominant electronic mechanism driving the formation of superconductivity in $\theta = 5.08^{\circ}$ twisted WSe$_2$ and demonstrates that nesting properties of the Fermi surface sheets near the higher-order van-Hove point cause an asymmetric density dependence of the spin ordering as the density is varied across the van-Hove line, in good agreement with experimental observations. We show how the region of superconducting and magnetic order evolves within the two-dimensional phase space of displacement field and electronic density as twist angle is varied between $4^{\circ} \dots 5^{\circ}$.