Revisitation of superconductivity in K$_2$Cr$_3$As$_3$ based on the six-band model

TL;DR

This study revisits the superconducting pairing symmetry in K$_2$Cr$_3$As$_3$ using a six-band model, confirming previous findings that triplet p_z-wave pairing driven by ferromagnetic fluctuations is dominant.

Contribution

It extends previous three-band model analysis to a six-band model, demonstrating the robustness of the p_z-wave pairing symmetry in K$_2$Cr$_3$As$_3$.

Findings

Triplet p_z-wave pairing is the leading symmetry in realistic parameters.

The six-band model results agree with the three-band model, indicating model independence.

Ferromagnetic fluctuations drive the p_z-wave pairing.

Abstract

We investigate the pairing symmetry of the newly synthesized quasi-one-dimension K$_2$Cr$_3$As$_3$ superconductor based on the six-band model. We adopt standard random-phase-approximation to study the Hubbard-Hund model of the system. Our results confirm the conclusions obtained from our previous three-band model: the triplet $p_z$ and $f_{y^3-3x^2y}$ wave pairings serve as the leading pairing symmetries in the weak and strong Hund's rule coupling regimes, respectively. For physically realistic parameters, the triplet $p_z$-wave pairing driven by ferromagnetic fluctuations is the leading pairing symmetry of the system. The consistency between the results of these two models suggests that the obtained $p_z$-wave pairing symmetry is physical and model-independent.