Symmetry of Hole States in Superconducting Oxides: Correlation withTc

Despite their small occupancy, the apical oxygen $p_z$ states have the indirect effect of modifying the relative occupancy of holes in states with different local symmetries in the Cu${\mathrm{O}}_2$ planes. A well-defined correlation is found between the maximum critical temperature $T_c^{max}$ of various cuprates and the excess of holes in states with local $a_1$ symmetry with respect to the doping ${\delta }^{max}$ at which $T_c^{max}$ is obtained for each compound. Implications for superconductivity models are discussed.