  In this study, we examine the superconducting instability of a
quasi-one-dimensional lattice in the Hubbard model based on the random-phase
approximation (RPA) and the fluctuation exchange (FLEX) approximation. We find
that a spin-singlet pair density wave (PDW-singlet) with a center-of-mass
momentum of $2k_F$ can be stabilized when the one-dimensionality becomes
prominent toward the perfect nesting of the Fermi surface. The obtained pair is
a mixture of even-frequency and odd-frequency singlet ones. The dominant
even-frequency component does not have nodal lines on the Fermi surface. This
PDW-singlet state is more favorable as compared to RPA when self-energy
correction is introduced in the FLEX approximation.
