Orbital entanglement mechanism of unconventional supercondcutivity

The widely held notion that the superconducting holes in cuprates reside in Cu d_x²-y² orbitals is incorrect, because two-hole correlations responsible for superconductivity are not described by the molecular orbital approximation. We utilize Hubbard model to show that insted, the nearest-neighbor d₂₊ and d_2- Cu orbitals become entangled due to orbitally-selective virtual hopping onto the p₊, p_- orbitals of oxygens shared by Cu neighbors. Without doping, these correlations lead to the Mott state or orbital antiferromagnetism. Doping suppresses these states, and the ground state becomes orbitally entangled singlet-like with a residual gauge symmetry. We provide thermodynamic arguments that the gauge symmetry becomes broken at sufficiently low temperature due to the collective correlation effects, resulting in the onset of superconductivity. We expect that the proposed orbital entanglement mechanism explains superconductivity in other unconventional superconductors, including SrTiO₃, iron pnictides and twisted multilayer graphene, and elucidates their direct connection with ferromagnetism, which can be described as condensation of orbitally-entangled spin triplets. Our analysis also provids specific guidance in the search for better high-temperature superconductors.