Onset of spin-valley order and Stoner boundaries in twisted WSe$_2$

Abstract

We investigate spin-valley instabilities and their connection to the magnetically ordered states recently observed in the twisted bilayer dichalcogenide WSe$_2$ at a $5^o$ twist angle. Starting from an effective three-orbital faithful Wannier model for the spin-locked moir\'e bands, combined with orbital-dependent Hubbard interactions, we analyze the evolution of magnetic instabilities as a function of carrier density using the matrix random phase approximation (mRPA) approach. By computing the Stoner boundary lines from the spin-valley susceptibilities over the electric-field by hole filling phase diagram, we show that the spin-valley instabilities result in ordered states in the region close to the Lifshitz transition at the topmost moir\'e valence band, marked by crossing of the Van Hove singularity in the density of states. These spin-valley ordered states are dominated by interorbital spin-valley-flips involving the $MM$ and $MX$ moir\'e orbitals and occur at different momenta in each side of the Van Hove line, indicating a distinct spatial dependence of the spin-valley order parameter depending on the hole filling. Moreover, the corresponding Stoner boundaries exhibit strong fluctuations on its flanks, which can favor superconducting states in the regions close to the spin-valley-ordered ones. This mechanism provides a natural description for a reentrant superconducting dome consistent with the experimental results. As such, our results suggest spin-valley fluctuations near the Van Hove line as the microscopic origin of the reentrant superconductivity in twisted WSe$_2$.