Effects of fermion-fermion interactions and impurity scatterings on fermion velocities in the line-nodal superconductors

We investigate the roles of both fermion-fermion interactions and impurities in pinning down the fates of fermion velocities in the line-nodal superconductors. Distinct sorts of four-fermion interactions and impurities as well as competitions among them are unbiasedly taken into account by adopting renormalization group approach. We firstly derive the coupled evolutions of all interaction parameters. Whether and how the interplay between fermionic interactions and impurities affects fermion velocities are then carefully studied. After performing the detailed analysis, we find the low-energy fates of fermion velocities are heavily dictated by fermion-fermion interactions. In addition to preserving isotropic, fermion velocities hinging sensitively upon initial values of interaction parameters can either exhibit extremely anisotropic or flow to certain finite anisotropy. With impurities being switched on, we reach that the behaviors of fermion velocities at clean limit are considerably robust. This indicates that fermion-fermion interactions dominate over the impurities in the low-energy regime. Moreover, several physical implications including the density of states and compressibility of fermionic quasiparticles are substantially modified due to the significant renormalization of fermion velocities in the low-energy regime. Graphical abstract