Interplay of single particle and Cooper pair tunnelings on the superconducting state of layered high- Tc cuprates

Abstract

In the present paper we report the interplay of single particle tunneling and Cooper pair tunneling on the low temperature superconducting state of layered high- T c cuprate superconductors. For this a microscopic model Hamiltonian has been considered that incorporates the intra-planar interactions along with contributions corresponding to the coupling between the planes in the form of single particle tunneling as well as Josephson Cooper pair tunneling. The expressions of the superconducting order parameter and the out-of-plane correlation parameter which describes the hopping of a particle from one layer to another layer in the superconducting state, are obtained as a function of various parameters of the model Hamiltonian within the BCS formalism using the Green’s function technique for a bilayer cuprate. It is found that the superconducting order parameter at zero temperature is robust against single particle tunneling while the Cooper pair tunneling between the layers enhances superconducting order parameter and provides favorable conditions for the formation of Cooper pairs within the planes. We have also calculated the out-of-plane contributions to the superconducting condensation energy which is in agreement with the existing calculations on the condensation energy of bilayer cuprates from the specific heat and the c-axis penetration depth measurements.