Effect of Next-Nearest-Neighbor Electron Hopping on Superconducting Gap of Cuprate Superconductors

We study here a single band Hamiltonian model to describe the effect of next-nearest-neighbor (NNN) electron hopping on superconducting gap in Cuprates. The Hamiltonian consists of nearest-neighbor (NN) and next-nearest-neighbor (NNN) electron hopping integrals between the copper sides. By taking d-wave pairing symmetry into account, BCS type superconducting interaction is studied. By applying Zubarev's Green function technique, the total Hamiltonian is solved. From the correlation function, the temperature-dependent superconducting gap (SC) equation is derived and is computed self-consistently by using technique 100 x 100 grid points of the electron momentum. By varying SC coupling, chemical potential, J-T coupling parameter and second-nearest-neighbor electron hopping integral, the evolution of the order parameter is investigated.