Superconductivity in monolayer and few-layer graphene: III Impurity-induced subgap states and quasi-particle interference patterns

TL;DR

This paper investigates how impurities affect the energy spectrum and interference patterns in superconducting graphene, revealing signatures that distinguish pairing symmetries and spin states.

Contribution

It provides a detailed analysis of impurity-induced subgap states and interference patterns in various superconducting pairing symmetries in graphene.

Findings

Scalar impurities produce two subgap states in most pairings.

Magnetic impurities can induce two or four subgap states depending on pairing symmetry.

Spin polarization of subgap states helps identify pairing type.

Abstract

We consider the most energetically favorable symmetry-allowed spin-singlet and spin-triplet superconducting pairing symmetries in monolayer and few-layer graphene, and for each calculate the energy spectrum in the presence of a scalar or magnetic impurity. We find that two doubly degenerate subgap states exist for scalar impurities for all types of pairing, except for the spin-singlet $s$-wave state. For magnetic impurities, two or four subgap states may form depending on the order parameter symmetry. We find that the spin polarization of these states allows one to distinguish between spin-singlet and triplet pairing, for example, only the spin-triplet states show opposite-energy subgap states with the same spin. We also calculate the quasi-particle interference patterns associated with the subgap states and find that they exhibit features that could distinguish between different types of pairing symmetries, especially a breaking of rotational symmetry for nodal states, stronger for the spin-singlet $d_{xy}$ and $d_{x^2-y^2}$ than for the spin-triplet $p_x$ and $p_y$ states.