Microscopic study of the role of second nearest neighbour spin density wave coupling and electron hopping on superconducting gap

Abstract

We report here a tight binding single band model Hamiltonian to study the role of spin density wave interaction and superconductivity. The Hamiltonian consists of nearest and next nearest neighbour electron hopping between the copper sides. The spin density wave interaction also includes nearest-neighbour and the next-nearest-neighbour spin interactions within a mean field approximation. BCS type superconducting interaction is considered taking d-wave pairing symmetry. By using Zubarev's Green function technique the Hamiltonian is solved. The antiferromagnetic and the superconducting gap equations are derived from the correlation functions and are solved self-consistently technique 100 × 100 grid points of the electron momentum. The evolution of these two order parameters are investigated by varying hole doping concentration, superconducting coupling, spin density wave coupling and second nearest neighbour electron hopping integrals.