Probe-type of superconductivity by impurity in materials with short coherence length: the s-wave and $\eta$-wave phases study

TL;DR

This study investigates how a single non-magnetic impurity affects superconducting states with s-wave and η-wave symmetries in materials with short coherence lengths, revealing local gap enhancements and oscillations.

Contribution

It provides a detailed analysis of impurity effects on both s-wave and η-wave superconductivity using the Penson-Kolb-Hubbard model with self-consistent Bogoliubov-de Gennes equations.

Findings

Local superconducting gap enhancement at impurity sites.

Long-range oscillations in energy gap and order parameter.

Distinct features in local-energy gap peaks for η-phase.

Abstract

The effects of a single non-magnetic impurity on superconducting states in the Penson-Kolb-Hubbard model have been analyzed. The investigations have been performed within two steps: (i) the homogeneous system is analysed using the Bogoliubov transformation, whereas (ii) the inhomogeneous system is investigated self-consistent Bogoliubova-de Gennes equations (by exact diagonalization and the kernel polynomial method). We analysed both signs of pair hopping, which correspond to s-wave and $\eta$-wave superconductivity. Our results show that an enhancement of the local superconducting gap at the impurity-site occurs for both cases. We obtained that Cooper pairs are scattered (at the impurity site) into the states which are from the neighborhoods of the states, which are commensurate ones with the crystal lattice. Additionally, in the $\eta$-phase there are peaks in the local-energy gap (in momentum space), which are connected with long-range oscillations in the spatial distribution of the energy gap, superconducting order parameter as well as effective pairing potential. Our results can be contrasted with the experiment and predicts how to experimentally differentiate these two different symmetries of superconducting order parameter by scanning tunneling microscopy technique.