Effects of the interplay between fermionic interactions and disorders in the nodal-line superconductors

TL;DR

This study uses renormalization group analysis to explore how fermionic interactions and various disorders influence the low-energy behavior of noncentrosymmetric nodal-line superconductors, revealing complex interplay effects.

Contribution

It provides a detailed analysis of the combined effects of fermionic interactions and multiple disorder types on the low-energy properties of nodal-line superconductors, including disorder relevance and velocity saturation.

Findings

Fermion velocities approach saturated values at low energies.

Certain disorders become relevant or irrelevant depending on conditions.

Interactions and disorders jointly shape low-energy behaviors.

Abstract

We study the interplay between fermion-fermion interactions and disorder scatterings beneath the superconducting dome of noncentrosymmetric nodal-line superconductors. With the application of renormalization group, several interesting low-energy behaviors are extracted from the coupled equations of all interaction parameters. At the clean limit, fermion-fermion interactions decrease with lowering the energy scales but conversely fermion velocities climb up and approach certain saturated values. This yields a slight decrease or increase of the anisotropy of fermion velocities depending upon their initial ratio. After bringing out four kinds of disorders designated by the random charge ($\Delta_{1}$), random mass ($\Delta_{2}$), random axial chemical potential ($\Delta_{3}$), and spin-orbit scatterers ($\Delta_{4}$) based on their own unique features, we begin with presenting the distinct low-energy fates of these disorders. For the presence of sole disorder, its strength becomes either relevant ($\Delta_{1,4}$) or irrelevant($\Delta_{2,3}$) in the low-energy regime. However, the competition for multiple sorts of disorders is capable of qualitatively reshaping the low-energy properties of disorders $\Delta_{2,3,4}$. Besides, it can generate an initially absent disorder as long as two of $\Delta_{1,2,3}$ are present. In addition, the fermion-fermion couplings are insensitive to the presence of $\Delta_4$ but rather substantially modified by $\Delta_1$, $\Delta_2$, or $\Delta_3$, and evolve towards zero or certain finite non-zero values under the coexistence of distinct disorders. Furthermore, the fermion velocities flow towards certain finite saturated value for the only presence of $\Delta_{2,3}$ and vanish for all other situations. As to their ratio, it acquires a little increase once the disorder is subordinate to fermionic interactions, otherwise keeps some fixed constant.