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

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.