Exotic Superconductivity in the Extended Attractive Hubbard Model

Abstract

We show that the extended attractive Hubbard model on a square lattice hosts a variety of superconducting phases, including exotic mixed-symmetry phases with $d_{x^2-y^2} + {\rm i} [s + d_{x^2+y^2}]$ and $ d_{x^2-y^2} + p_{x}$ symmetries, and a novel $p_x + {\rm i} p_y$ state. The calculations are performed within the mean-field Bogoliubov-deGennes (BdG) framework. The ground states of the BdG Hamiltonian are obtained via a minimization scheme that does not impose symmetry constraints on the superconducting solutions, hence allowing a mixing of $s$-, $p$- and $d$-wave order parameters. Our results show that extended attractive Hubbard model can serve as an effective model for investigating properties of exotic superconducting states.