Effect of dilute impurities on short graphene Josephson junctions

We study the effect of a dilute homogeneous spatial distribution non-magnetic impurities on equilibrium supercurrent sustained by ballistic graphene Josephson junction in short limit. Within Dirac-Bogoliubov-de Gennes approach and modeling Anderson model we derive its power spectrum. find modification current-phase relation with reduction skewness induced disorder, nonmonotonic temperature dependence critical current. The potentialities spectrum for accurate spectroscopy hybridized Andreev bound states-impurities are highlighted. In low limit, zero frequency thermal noise directly probes spectral function at Fermi energy.