Perturbation Theory for a Repulsive Hubbard Model in Quasi-One-Dimensional Superconductors

We investigate pairing symmetry and a transition temperature in a quasi-one-dimensional repulsive Hubbard model. We solve the Eliashberg equation using the third-order perturbation expansion with respect to the on-site repulsion $U$. We find that when the electron number density is shifted from the half-filled, a transition into unconventional superconductivity is expected. When one dimensionality is weak, a spin-singlet state is favorable. By contrast, when one dimensionality is strong and electron number density is far from the half-filled, a spin-triplet state is stabilized. Finally, we discuss the possibility of unconventional superconductivity caused by the on-site Coulomb repulsion in $\beta$-Na$_{0.33}$V$_2$O$_5$.