Electronic structure ofCuO2sheets and spin-driven high-Tcsuperconductivity

Abstract

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 ${U}_{d}$.The coexisting spin and carrier systems interact strongly, the most important cause being a virtual process involving the Cu(${d}^{10}$) configuration, which is lowered in energy by Coulomb interactions with the carrier. This process can produce carrier transport with and without creating spin deviations and stabilizes holes in the oxygen ${p}_{\ensuremath{\sigma}}$ orbitals. We find that the carriers are neither weakly coupled free particles nor spin polarons, but are something new: ``spin hybrids,'' consisting of a coherent and nonperturbative mixture of local spin-orbital electronic configurations, some of which represent deviations in the local AF order. A model Hamiltonian that describes the spin-hybrid carriers shows that the probability of finding a spin deviation associated with an isolated carrier quasiparticle is large (30--40 %). We find spin-driven electronic pairing in the Cooper sense between the spin-hybrid quasiparticles. Retarded interactions are possible, but we also find direct attractive unretarded interactions at \ensuremath{\sim}3--4 Cu-O spacings, driven by carrier-enhanced superexchange, which is larger than the Coulomb correction. These interactions cause extended s-wave and d-wave pairing and lead to a pairing Hamiltonian reminiscent of BCS theory which is, however, only two-dimensional. The possible role of Josephson tunneling in the third dimension is also discussed.