Superconducting gap symmetry determined by the electron density

In this work, a comparative study of pairing and superconducting states in square lattices with s-, p- and d-symmetries is performed within the BCS formalism and a generalized Hubbard model, in which correlated-hopping interactions are considered in addition to the repulsive Coulomb interactions. The two-particle analysis reveals the importance of the van Hove singularity in the formation of pairs and then the two-particle states with different pairing symmetry have their maximum binding energies at the same hopping strength. This feature is confirmed by the superconducting critical temperature (T c) calculation at the low-density regime. However, a different picture is found for the high-density regime, i.e., the maxima of the s- and d-channel T c split from the expected value and no p-wave superconducting state is found. This study suggests that the three superconducting symmetries can be analyzed within a single framework