Role of Cu d-d inter-orbital electron correlation on the out-of-plane conduction in cuprates

Abstract

In the present paper we study a model which is relevant to an analysis of the effects of the Cu d-d inter-orbital electron correlation on the motion of charge carriers along c-axis in high-T_c cuprates. For this a microscopic model Hamiltonian for the three atom cluster CuO₂ which incorporates the essential features of the basic unit of high-T_c cuprates has been considered. The model Hamiltonian for this three atom cluster includes various in-plane and out-of-plane orbital energies, their intra- and inter-orbital Coulomb interactions relevant for the electrons in the cluster. The out-of-plane correlation which appears when we consider the hopping of a hole from the Cu 3d_3z²-r² to apical O 2p_z orbitals has been calculated using the Green's function technique. The equation of motion for the relevant Green's function contains higher order Green's functions and we evaluate the correlation parameter relevant to motion for a hole along the c-axis by using suitable decoupling approximations. It has been found through numerical calculations that the out-of-plane correlations depend on the intra- and inter-orbital Coulomb interactions, the out-of-plane orbital energies, hole occupancy and on temperature. Finally, the relevance of the out-of-plane correlation parameter for present three atom CuO₂ cluster model to the c-axis conductivity of the bulk high-T_c cuprate systems has been pointed out.