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 centerof-mass momentum of 2kF 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 oddfrequency 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.
We study superconductivity and surface Andreev bound states in helical crystals. We consider the interlayer pairings along the helical hopping and investigate the surface local density of states on the (001) and zigzag surfaces for all the possible irreducible representations. There are three and four irreducible representations exhibiting the zero energy peaks in the local density of states at the (001) and zigzag surfaces of helical lattices, respectively. By calculating the one dimensional winging number, we show that these appearances of the zero energy peaks stem from the surface Andreev bound states.
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