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

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.