We solve the Cooper problem in a cuprate lattice by utilizing a three-band model. We determine the ground state of a Cooper pair for repulsive on-site interactions, and demonstrate that the corresponding wave function has an orbital $d_{ x^2-y^2}$ symmetry. We discuss the influence of next-nearest-neighbor tunneling on the Cooper pair solution, in particular the necessity of next-nearest-neighbor tunneling for having $d$-wave pairs for hole-doped systems. We also propose experimental signatures of the $d$-wave Cooper pairs for a cold-atom system in a cuprate lattice.
Categories: cond-mat.supr-con cond-mat.quant-gas physics.atom-ph quant-ph
