Coexistence of superconductivity and charge density wave in a correlated regime

To investigate the coexistence of superconductivity and charge density wave (CDW) in a correlated regime, we employ the Green's functions formalism, as well as the Hubbard-I approximation, as a way to introduce the correlations into the problem, in the form of a repulsive Coulomb interaction $U$. In addition, we investigate the effects of second-nearest neighbor hopping $t_1$ on a pure CDW state. The analysis of the results show that, for small values of $t_1$, both CDW and superconducting gaps compete for the same region on the Fermi surface. The increase of $t_1$ decreases the competition and may lead the system to a coexistence regime. Effects of temperature in the coexistence regime, are also investigated.