Spin-triplet and spin-singlet superconductivity in the Hubbard model on a triangular lattice

Within third-order perturbation theory, we discuss the possibility of spin-triplet and spin-singlet superconductivities in a two-dimensional Hubbard model on a triangular lattice for some model parameters corresponding to the heavy-fermion superconductors UM₂Al₃ (M = Pd,Ni) and organic superconductors under uniaxial strain. In the model of the heavy-fermion superconductors UM₂Al₃ (M = Pd,Ni), when we vary the symmetry in the dispersion of the bare energy band from D₂ to D₆, spin-singlet superconductivity in the D₂-symmetric system is suppressed and we obtain spin-triplet superconductivity in the nearly D₆-symmetric system. We point out the possibility that the results obtained correspond to the difference between the superconductivity of UPd₂Al₃ and that of UNi₂Al₃. In the model of organic superconductors under uniaxial strain, when we increase the diagonal hopping integral to above 1.2, we obtain the tendency for spin-triplet superconductivity to emerge. In all cases mentioned above, it is found that the vertex correction terms, which are not included in the interaction mediated by the spin fluctuation, are essential for realizing the spin-triplet pairing.