Critical behavior around the fixed points driven by fermion-fermion interactions and disorders in the nodal-line superconductors

We systematically investigate the intricate interplay between short-range fermion-fermion interactions and disorder scatterings beneath the superconducting dome of noncentrosymmetric nodal-line superconductors. Employing the renormalization group that unbiasedly treats all kinds of potential degrees of freedom, we establish energy-dependent coupled flows for all associated interaction parameters. Decoding the low-energy information from these coupled evolutions leads to the emergence of several intriguing behavior in the low-energy regime. At first, we identify eight distinct types of fixed points, which are determined by the competition of all interaction parameters and dictate the low-energy properties. Next, we carefully examine and unveil distinct fates of physical implications as approaching such fixed points. The density of states of quasiparticles displays a linear dependence on frequency around the first fixed point, while other fixed points present diverse frequency-dependent behavior. Compressibility and specific heat exhibit unique trends around different fixed points, with the emergence of non-Fermi-liquid behavior nearby the fifth fixed point. Furthermore, after evaluating the susceptibilities of the potential states, we find that a certain phase transition below the critical temperature can be induced when the system approaches the fifth fixed point, transitioning from the nodal-line superconducting state to another superconducting state. This research would enhance our understanding of the unique behavior in the low-energy regime of nodal-line superconductors.