Theory of topological superconductivity and antiferromagnetic correlated insulators in twisted bilayer WSe2

Since the very recent discovery of unconventional superconductivity in twisted WSe₂ homobilayers at filling ν = - 1, considerable interest has arisen in revealing its mechanism. In this paper, we developed a three-band tight-binding model with non-trivial band topology by direct Wannierization of the low-energy continuum model. Incorporating both onsite Hubbard repulsion and next-nearest-neighbor attraction, we then performed a mean-field analysis of the microscopic model and obtained a phase diagram qualitatively consistent with the experiment results. For zero or weak displacement field, the ground state is a Chern number C = ± 2 topological superconductor in the Altland-Zirnbauer A-class (breaking time-reversal but preserving total S_z symmetry) with inter-valley pairing dominant in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow><mml:mi>x</mml:mi> <mml:mi>y</mml:mi></mml:mrow> </mml:msub> <mml:mo>±</mml:mo> <mml:mi>i</mml:mi> <mml:msub><mml:mrow><mml:mi>d</mml:mi></mml:mrow> <mml:mrow> <mml:msup><mml:mrow><mml:mi>x</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> <mml:mo>-</mml:mo> <mml:msup><mml:mrow><mml:mi>y</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:msub> </mml:math> -wave (mixing with a subdominant p_x ∓ ip_y-wave) component. For a relatively strong displacement field, the ground state is a correlated insulator with the 120° antiferromagnetic order. Our results provide new insights into the nature of the twisted WSe₂ systems and suggest the need for further theoretical and experimental explorations.