Doping dependence of chiral superconductivity in near $45^\circ$ twisted bilayer cuprates

Abstract: We study a one-band Hubbard model for a twisted cuprate bilayer with a twist angle of 43.6$^\circ$ and a moire cell containing 58 sites. We use the variational cluster approximation (VCA), which treats short-range correlations exactly and leads, in single layers, to a dome of d-wave superconductivity away from half-filling from strong on-site repulsion alone. We find a time-reversal-symmetry (TRS) breaking phase in a small doping interval in the overdoped region when interlayer tunneling is strong enough. Contrary to expectations, being closer to the $45^{\circ}$ twist angle does not expand this TRS region compared to a previous study [Phys. Rev. B 105, 245127 (2022)] on a $53^{\circ}$ twist angle. This is attributed to the fact that the two superconducting states in competition have almost identical nodal structures.