d_{3z^2-r^2} Orbital in high-Tc cuprates: Excitonic spectrum,   metal-insulator phase diagram, optical conductivity and orbital character of   doped holes
  The single-site dynamical mean-field approximation is used to solve a model of high-Tc cuprate superconductors which includes both d_{x^2-y^2} and d_{3z^2-r^2} orbitals on the Cu as well as the relevant oxygen states. Both T (with apical oxygen) and T' (without apical oxygen) crystal structures are considered. In both phases, inclusion of the d_{3z^2-r^2} orbital is found to broaden the range of stability of the charge transfer insulating phase. For equal charge transfer energies and interaction strengths, the T' phase is found to be less strongly correlated than the T phase. For both structures, d-d excitons are found within the charge-transfer gap. However, for all physically relevant dopings the Fermi surface is found to have only one sheet and the admixture of d_{3z^2-r^2} into ground state wave function remains negligible (<5%). Inclusion of the extra orbitals is found not to resolve the discrepancy between computed and observed conductivity in the insulating state. 
Xin Wang, Hung The Dang, and Andrew J. Millis
cond-mat.supr-con cond-mat.str-el