Stripe antiferromagnetism and chiral superconductivity in tWSe$_2$
The layer-dependent Hamiltonians of parallel-stacked MoTe$_2$ and WSe$_2$ homobilayer moir\'e materials are topologically non-trivial, both in real space and in momentum space, and have been shown to support integer and fractional quantum anomalous Hall states, as well as antiferromagnetic and superconducting states. Here, we address the interplay between the antiferromagnetic and superconducting states observed in tWSe$_2$ when the Fermi level is close to its $M$-point van Hove singularity and the displacement field is small. We combine DFT with path-integrals to construct a minimal moir\'e band model that accounts for lattice relaxation along the $c$-axis and perform Hartree-Fock calculations to identify competing charge and spin ordered states. For tWSe$_2$ at $\theta=2.7^\circ$ and $\theta=3.65^\circ$, we find that a layer antiferromagnet (AFM), a stripe spin-density-wave (SDW), and the ferromagnetic Chern insulator (FM) are the primary candidates for the ground state at zero displacement field, and argue that antiferromagnetic spin interactions on the next neighbor bond $J_2$ can induce a time-reversal symmetry breaking chiral superconducting state.