Electronic structure ofCuO2sheets and spin-driven high-Tcsuperconductivity

Energy parameters for a ${\mathrm{CuO}}_2$ sheet, taken to be prototypic of the high-temperature superconductors, are derived from semiempirical and ab initio sources. Intra-atomic Coulomb interactions ($U_i$) are large, but interatomic Coulomb terms and direct oxygen-oxygen transfer integrals are also very important. These energies dictate a two-band extended Hubbard Hamiltonian which cannot obviously be simplified. With Cu($d^{10}$)O($p^6$) as the vacuum state, interatomic Coulomb interactions create a potential well resulting in hole localization when there is one hole per ${\mathrm{CuO}}_2$ unit cell, so that the Cu($d^9$) valence is dominant. A spin-(1/2 Heisenberg system thus exists independent of the presence of carriers due to the poor screening in these materials. We compute the Cu-Cu superexchange energy J from the other parameters and find good agreement with empirically derived values, provided the inclusion direct Cu-O exchange. Because of the relatively large value of J, we assume local antiferromagnetic (AF) order. Itinerent carriers exist on the oxygen sublattice because of the large Cu $U_d$.