Energy parameters for a CuO2 sheet, taken to be prototypic of the high-temperature superconductors, are derived from semiempirical and ab initio sources. Intra-atomic Coulomb interactions (Ui) 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(d10)O(p6) as the vacuum state, interatomic Coulomb interactions create a potential well resulting in hole localization when there is one hole per CuO2 unit cell, so that the Cu(d9) 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 Ud. The coexisting spin and carrier systems interact strongly, the most important cause being a virtual process involving the Cu(d10) 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 pσ 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 ∼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.
ASJC Scopus subject areas
- Condensed Matter Physics