Optimal superconductivity in twisted bilayer WSe$_2$ where the Van Hove singularity crosses half-filling

Abstract: The recent discovery of unconventional superconductivity has pointed to twisted WSe$_2$ bilayer as a versatile platform for studying the correlated and topological phases of matter. Here we analyze the effect of the displacement field and electron interactions on the formation of a topological paired state in twisted WSe$_2$. Our approach is based on the effective single band $t$-$J$-$U$ model supplemented with intersite Coulomb interaction term and treated within the Gutzwiller approximation. We show that the superconducting phase is stabilized in a small range of displacement fields where the Van Hove singularity crosses half-filling, which is in qualitative agreement with recent experimental data. According to our analysis, such a circumstance comes as a result of a subtle interplay between the large density of states of the Van Hove singularity, in combination with the renormalization effects that appear in the weak-to-moderate correlations regime. The two factors create favorable conditions for the SC pairing only in a small area of the phase diagram.