Eur. Phys. J. Plus (2023) 138: 607
https://doi.org/10.1140/epjp/s13360-023-04223-7

Regular Article

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

¹ Department of Physics, Tianjin University, 300072, Tianjin, People’s Republic of China
² Tianjin Key Laboratory of Low Dimensional Materials Physics and Preparing Technology, Tianjin University, 300072, Tianjin, People’s Republic of China

^c jing_wang@tju.edu.cn

Received: 26 December 2022
Accepted: 22 June 2023
Published online: 12 July 2023

Abstract

We carefully study the interplay between short-range fermion–fermion interactions and disorder scatterings beneath the superconducting dome of the noncentrosymmetric nodal-line superconductors. With the application of renormalization group, the energy-dependent coupled flows of all these associated interaction parameters are established after taking into account the potential low-energy physical ingredients including both kinds of fermionic interactions and disorder couplings as well as their competitions on the same footing. Encoding the low-energy information from these entangled evolutions gives rise to several interesting behaviors in the low-energy regime. 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 in the anisotropy of fermion velocities depending upon their initial ratio. After bringing out four kinds of disorders designated by the random charge (${\mathrm{\Delta }}_1$), random mass (${\mathrm{\Delta }}_2$), random axial chemical potential (${\mathrm{\Delta }}_3$), and spin-orbit scatterers (${\mathrm{\Delta }}_4$) 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 (${\mathrm{\Delta }}_{1,4}$) or irrelevant(${\mathrm{\Delta }}_{2,3}$) in the low-energy regime. However, the competition for multiple sorts of disorders is capable of qualitatively reshaping the low-energy properties of disorders ${\mathrm{\Delta }}_{2,3,4}$. Besides, it can generate an initially absent disorder as long as two of ${\mathrm{\Delta }}_{1,2,3}$ are present. In addition, the fermion–fermion couplings are insensitive to the presence of disorder ${\mathrm{\Delta }}_4$ but rather substantially modified by ${\mathrm{\Delta }}_1$, ${\mathrm{\Delta }}_2$, or ${\mathrm{\Delta }}_3$, and they evolve toward zero or certain finite nonzero values under the coexistence of distinct disorders. Furthermore, the fermion velocities flow toward certain finite saturated value for the only presence of ${\mathrm{\Delta }}_{2,3}$ and vanish for all other situations. As to their ratio, it acquires a little increase once the disorder is subordinate to fermion–fermion interactions, otherwise keeps some fixed constant.