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

TL;DR

This paper uses third-order perturbation theory to analyze pairing symmetry and transition temperatures in a quasi-one-dimensional Hubbard model, revealing conditions favoring spin-singlet or triplet superconductivity.

Contribution

It introduces a third-order perturbation approach to study unconventional superconductivity in a quasi-one-dimensional Hubbard model, highlighting the effects of electron density and dimensionality.

Findings

Spin-singlet favored when dimensionality is weak.

Spin-triplet stabilized at strong dimensionality and away from half-filling.

Potential relevance to superconductivity in $eta$-Na$_{0.33}$V$_2$O$_5$.

Abstract

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$_5$.