Resonant impurity scattering in the unconventional superconductors

In this pedagogical review, I provide comparative studies of the impurity scattering effects on the two typical types of the unconventional superconductors: d-wave and ±s-wave superconductors. For the d-wave superconductor, the main effect of impurity scattering is the formation of the zero energy resonant state by the unitary scatters below Tc. Similarly, in the case of the ±s-wave superconductor, I show that impurity scattering of the unitary limit also forms a resonant bound state, however, not a zero energy but an off-centered bound state inside the superconducting (SC) gap, which modifies the density of states (DOS) of a fully opened gap to a V-shaped one mimicking the pure d-wave DOS. On the contrary, in the d-wave case, the zero energy bound state modifies the original V-shape DOS into a flat constant one near zero frequency. This contrasting behavior of the impurity effect can be useful to distinguish the gap symmetry of the newly discovered Fe-based superconductors. This contrasting behavior of two SC states with respect to the impurity scattering is demonstrated by numerical calculations of the density of states (DOS), NMR 1/T1 rate and Knight shift K(T)