Superconducting phase with the ($d+id$) order parameter in an ensemble of Hubbard fermions on the triangular lattice

In the framework of the $t{-}J_1{-}J_2{-}V$ model, the integral equation determining the order parameter $\Delta(p)$ of the superconducting phase is derived for an ensemble of strongly correlated fermions on a triangular lattice using the diagram technique for the Hubbard operators. Taking into account the interaction between the Hubbard fermions within two coordination spheres, we demonstrate that the exact analytical solution $\Delta_2(p)$ of this equation for the superconducting phase with the ($d_{x^2-y^2}+id_{xy}$) symmetry can be expressed as a superposition of two chiral basis functions. This gives rise to a new set of nodal points for the complex parameter $\Delta_2(p)$. Moreover, at some critical value $x_c$ of the charge carrier density, we obtain a gapless phase with six Dirac points. The passing of $x$ through $x=x_c$ is accompanied by the topological quantum transition corresponding to the change in the topological parameter $Q$.