Impurity effect as a probe for the pairing symmetry of graphene-based superconductors

TL;DR

This paper theoretically investigates how impurity effects can distinguish different pairing symmetries in graphene-based superconductors, revealing characteristic resonance peaks that serve as experimental probes.

Contribution

It provides a detailed analysis of impurity-induced in-gap states for various pairing symmetries, offering a new method to identify the pairing symmetry in graphene superconductors.

Findings

Sharp resonance peaks near impurities for $d+id$ and $p+ip$ symmetries at large chemical potential.

Robust in-gap states for $d+id$ symmetry as chemical potential decreases.

Absence of in-gap peaks for extended $s$-wave and $f$-wave symmetries.

Abstract

The single impurity effect on the graphene-based superconductor is studied theoretically. Four different pairing symmetries are discussed. Sharp resonance peaks are found near the impurity site for the $d+id$-wave pairing symmetry and the $p+ip$-wave pairing symmetry when the chemical potential is large. As the chemical potential decreases, the in-gap states are robust for the $d+id$ pairing symmetry while they disappear for the $p+ip$ pairing symmetry. Such in-gap peaks are absent for the fully gapped extended $s$-wave pairing symmetry and the nodal $f$-wave pairing symmetry. The existence of the in-gap resonance peaks can be explained well based on the sign-reversal of the superconducting gap along different Fermi pockets and by analyzing the denominator of the $T$-matrix. All of the features can be accessed by the experiments, which provide a useful probe for the pairing symmetry of graphene-based superconductors.