Third Order Perturbation Analysis of Pairing Symmetry in Two-Dimensional Hubbard Model

TL;DR

This paper uses third-order perturbation theory to analyze superconducting pairing symmetries in a 2D Hubbard model, highlighting the importance of vertex corrections in determining dominant pairing states.

Contribution

It introduces third-order perturbation analysis to study pairing symmetries, emphasizing the role of vertex corrections in the Hubbard model.

Findings

p-wave pairing is stable at low to intermediate densities

d_{x^2-y^2}-wave pairing dominates near half-filling

vertex correction is crucial for p-wave pairing stability

Abstract

We study the superconducting instabilities of singlet and triplet pairing in a two-dimensional Hubbard model on the basis of the third-order perturbation theory (TOPT). We investigate the effect of the vertex correction that is given by TOPT, comparing with the study with only the second-order effective interaction. In our results, a stable p-wave pairing state spreads from low to intermediate electron density. A dx2-y2-wave pairing is dominant for the high density near a half-filling. It is shown that the vertex correction plays an essential role in making the p-wave pairing state dominant.