Single magnetic impurity effects in graphene based superconductors

The magnetic impurity effects and the existence of bound states (i.e. Yu-Shiba-Rusinov states) in superconductors have been a topic of great interest. Recently, the existence of Yu-Shiba-Rusinov states in graphene-based superconducting materials has been successfully observed in the laboratory. This paper establishes an effective Hamiltonian in real space to describe the superconducting state of graphene materials, considering a single magnetic impurity. It constructs the Bogoliubov-de Gennes (BdG) equation and performs self-consistency calculations on the superconducting order parameter. On this basis, the paper theoretically investigates the effects of magnetic impurities on graphene-like superconductors. The calculation results show that the Yu-Shiba-Rusinov state can only appear within the superconducting pairing symmetry of the traditional s-wave pairing. The position and strength of the bound state are related to the magnetic moment of the impurity, and it shows a notable electron-hole asymmetry. There are no bound states in the energy gap for other pairing symmetries. This theoretical calculation not only provides a reasonable explanation for experimental phenomena, but also demonstrates that the heterojunction system composed of graphene and traditional superconductors has an s-wave superconducting pairing induced by the proximity effect in the graphene layer.