Testing the Fully Gapped S-Wave Superconductor $$\hbox {cecu}_2\hbox {si}_2$$ CeCu 2 Si 2 by Impurity-Induced Intra-gap States

The fully gapped s-wave superconducting state, such as nodeless $$s^{\pm }$$ -wave and $$s^{++}$$ -wave, was proposed by recent experiments in the multiband superconductor $$\hbox {CeCu}_{2}\hbox {Si}_{2}$$ . In this paper, we study the problem within an effective two hybridization bands model obtained from the first principle calculations. Our results based on T-matrix approximation reveal that for $$s^{++}$$ -wave pairing, there are no intra-gap resonance states induced by a nonmagnetic impurity irrespective of the inter-band impurity scattering strength. However, in the case of sign-changing $$s^{\pm }$$ -wave pairing, we find two intra-gap resonance states appearing at positive and negative energies around the Fermi energy with introducing inter-band impurity scattering. These features can be readily verified by scanning tunneling microscopy/spectroscopy and are proposed to identify the sign-changing fully gapped superconducting state in $$\hbox {CeCu}_{2}\hbox {Si}_{2}$$ at ambient pressure.