How standard DFT reveals the microscopic orbital picture of strongly correlated cuprate superconductors

Cuprate high-temperature superconductors are prototypical strongly correlated systems. Clarifying the complex orbital interactions within these systems has been one of the greatest challenges in condensed matter physics. Because the coupling between orbital bands cannot be disentangled, conventional density functional theory (DFT) has struggled to provide a microscopic picture of individual orbital bands. To investigate the contribution of core-orbital coupling (COC) to strong correlation—which is neglected by the adiabatic approximation in DFT—this paper extracts the ubiquitous pyramidal layer (based on the CuO 2 plane oxygens and neighboring rare-earth ions) and uses inert gas atom substitution (He replacing O 2 s , Ne replacing RE p ) to construct a minimal model that isolates COC. Using standard DFT to calculate supercells of varying sizes (n×n, n = 1–15) to simulate doping, we reveal that COC can generate stable spin-singlet pairs (Px, Py, Pz) formed through s – p hybridization, with a binding energy of approximately 0.2 eV. Within the CuO 2 plane, the Px/Py states form either linear long-range chains ( n = 2) or vortex-like patterns ( n ≥ 3), depending on the degree of translational symmetry breaking. The COC network is robust against up to 25% vacancies, may corresponding to the quantum critical point ( p = 0.25) in the cuprate doping phase diagram. Strong spin-orbit coupling leads to spin-momentum locking, stabilizing the spin-singlet configuration. These results show similarities with the resonating valence bond (RVB) theory, Kosterlitz-Thouless (KT) theory, and valence bond solid (VBS) picture, and also open up a practical route for using standard DFT tools to study orbital interactions in strongly correlated systems.