Electron or hole binding energy in Cu-O clusters: Exact diagonalization of the Emery Hamiltonian

Bednorz and Mueller's discovery of high Tc superconductivity spurred many suggestions regarding the mechanism for superconductivity in the high Tc superconductors. The high Tc values and the small isotope effect have stimulated very active research on various nonphonon pairing mechanisms. The most popular one today is the Emery model, which incorporates strong electron correlations in the high Tc superconductors. In this paper the authors are reporting a study of the ground state of the Emery Hamiltonian in two-dimensional Cu-O clusters for various carrier densities by an exact diagonalization method. The ground-state energy of two-dimensional Cu-O clusters consisting of 8 and 12 atoms with various occupation numbers is calculated numerically through an exact diagonalization of the Emery Hamiltonian. It is shown, for the first time, that there is an effective attraction not only for holes, but also for electrons in these clusters, over a wide range of parameter values. The stability with respect to phase separation is analyzed. The occupation numbers are calculated for the copper and oxygen orbitals. The spin-spin and density-density correlation functions are also calculated. The nature of the disruption of the antiferromagnetic order in the case of an electron doping is the same as in the case of a hole doping: the addition of one electron (or hole) to the insulating state causes a far greater disruption of the antiferromagnetic order than is caused by the subsequent addition of a second electron (or hole). The apparent reason for the attraction of two electrons is, as for holes, a decrease in the size of the regions in which the antiferromagnetic order is disrupted (and a corresponding lowering of the energy of the system) in the case in which the excess electrons (or holes) are close to each other