Local analysis of a single impurity on a graphene Josephson junction

In this paper, we investigate the local effects of a single impurity on the electron system of a short ballistic graphene Josephson junction. Within the Dirac–Bogoliubov–de Gennes approach, we systematically analyze the local electron density of states. Its behavior at subgap energies allows one to distinguish elastic and inelastic scattering processes and to identify the magnetic nature of the impurity. Moreover, the spatial dependence of the local density of states is a sensitive probe of microscopic processes yielding subgap impurity-induced bound states. The Fourier analysis allows one to recognize the wave vectors related to the momenta of the high-transmissive channels in ballistic graphene.