Optimal superconductivity in twisted bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>WSe</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> where the Van Hove singularity crosses half-filling

The recent discovery of unconventional superconductivity has pointed to twisted <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>WSe</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:msub> <b:mi>WSe</b:mi> <b:mn>2</b:mn> </b:msub> </b:math> . Our approach is based on the effective single band <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"> <c:mrow> <c:mi>t</c:mi> <c:mtext>−</c:mtext> <c:mi>J</c:mi> <c:mtext>−</c:mtext> <c:mi>U</c:mi> </c:mrow> </c:math> 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 correlation regime. The two factors create favorable conditions for the superconducting pairing only in a small area of the phase diagram.