Tuning topological superconductivity within the t−J−U model of twisted bilayer cuprates

We carry out a theoretical study of unconventional superconductivity in twisted bilayer cuprates (TBCs) as a function of electron density and layer twist angle. The bilayer $t\text{\ensuremath{-}}J\text{\ensuremath{-}}U$ model is employed and analyzed within the framework of a generalized variational wave function approach in the statistically consistent Gutzwiller formulation. The constructed phase diagram encompasses both a gapless $d$-wave state (reflecting the pairing symmetry of untwisted copper-oxides) and gapped $d+{\mathrm{e}}^{i\ensuremath{\varphi}}d$ phase that breaks spontaneously time reversal symmetry (TRS) and is characterized by a nontrivial Chern number. We find that the $d+{\mathrm{e}}^{i\ensuremath{\varphi}}d$ state occupies a nonconvex butterfly-shaped region in the doping versus twist-angle plane and demonstrate the presence of a reentrant TRS-breaking phase on the underdoped side of the phase diagram. This circumstance supports the emergence of topological superconductivity for fine-tuned twist angles in TBC away from ${45}^{\ensuremath{\circ}}$. Our analysis of the microscopically derived Landau free-energy functional points toward sensitivity of the superconducting order parameter to small perturbations close to the topological state boundary.