Correlation-Driven d-Wave Superconducting Dome from Pseudogap Spectral Reconstruction

Previous theoretical studies [Nat. Phys. {\bf 16}, 1175 (2020)] based on the Hatsugai-Kohmoto model have examined the stability of $s$-wave superconductivity in strongly correlated systems, demonstrating that correlations alone can substantially modify superconducting behavior. Motivated by this perspective, but going beyond these studies, we perform self-consistent microscopic calculations of $d$-wave superconductivity in strongly correlated systems by employing an exactly solvable correlated model that hosts a pseudogap phase and a partially flat band [Phys. Rev. Lett. {\bf 133}, 166501 (2024)]. We show that pseudogap correlations and superconducting order affect the low-energy spectrum in qualitatively different ways: the former leads to a momentum-localized suppression of spectral weight, whereas the latter induces a coherent reorganization of quasiparticle excitations. Moreover, we demonstrate that the interplay between superconducting order and pseudogap correlations naturally generates a superconducting dome in the temperature-doping phase diagram, with optimal doping located near the quantum critical point separating the pseudogap and metallic phases. Furthermore, $d_{x^2-y^2}$-wave superconductivity is found to be remarkably robust, remaining energetically dominant over both $d_{xy}$-wave and $s$-wave pairing channels across a wide doping range. Our results offer a potential route for a direct and controlled connection between pseudogap correlations and the emergence of the superconducting dome in cuprates.