Probing Sign-Changing Order Parameters via Impurity States in unconventional superconductors: Implications for La$_3$Ni$_2$O$_7$ Superconductors with interlayer pairing

Abstract

Motivated by the desire to investigate the fundamental relationship between impurity-induced states and the sign change of the superconducting order parameter, as well as to explore the impurity effects in Ruddlesden-Popper nickelate superconductors with interlayer pairing, we employ the $T$-matrix approach to study single impurity scattering in unconventional superconductors. Our work focuses on two distinct pairing scenarios: intralayer $d$-wave pairing and interlayer $s$-wave pairing. For systems with intralayer $d$-wave pairing, we establish an intrinsic connection between the $d$-wave pairing symmetry and the emergence of mid-gap resonant states. Through a combination of analytical derivations and numerical simulations, we demonstrate that the appearance of in-gap states is directly linked to the sign reversal of the order parameter along the Fermi surface. In interlayer pairing systems, our results reveal the presence of pronounced resonant peaks, which can also be attributed to the sign-changing nature of the order parameter. We further extend our analysis to the bilayer nickelate superconductor La$_3$Ni$_2$O$_7$, providing a theoretical investigative of impurity effects in this material. Our findings not only elucidate the complex interplay between pairing symmetries and impurity-induced states in unconventional superconductors but also offer a powerful tool for probing the pairing mechanisms in nickelate-based high-temperature superconductors. This work lays the groundwork for future experimental and theoretical investigations into the unique electronic properties of these emerging materials.