Superconducting bilayer cuprates; condensation energy; Cooper pair tunneling.
In the present work, we report the interplay of single particle and Cooper pair tunnelings on the superconducting state of layered high-𝑇c cuprate superconductors. For this we have considered a model Hamiltonian incorporating the intra-planar interactions and the contributions arising due to the coupling between the planes. The interplanar interactions include the single particle tunneling as well as the Josephson tunneling of Cooper pairs between the two layers. The expression of the out-of-plane correlation parameter which describes the hopping of a particle from one layer to another layer in the superconducting state is obtained within a Bardeen–Cooper–Schriefer (BCS) formalism using the Green’s function technique. This correlation is found to be sensitive to the various parameter of the model Hamiltonian. We have calculated the out-of-plane contribution to the superconducting condensation energy. The calculated values of condensation energy are in agreement with those obtained from the speciﬁc heat and the 𝑐-axis penetration depth measurements on bilayer cuprates.