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We study the effect of a dilute homogeneous spatial distribution of non-magnetic impurities on the equilibrium supercurrent sustained by a ballistic graphene Josephson junction in the short junction limit. Within the Dirac Bogoliubov-de Gennes approach and modeling impurities by the Anderson model we derive the supercurrent and its equilibrium power spectrum. We find a modification of the current-phase relation with a reduction of the skewness induced by disorder, and a nonmonotonic temperature dependence of the critical current. The potentialities of the supercurrent power spectrum for accurate spectroscopy of the hybridized Andreev bound states-impurities spectrum are highlighted. In the low temperature limit, the supercurrent zero frequency thermal noise directly probes the spectral function at the Fermi energy.
Publication date: 
8 Mar 2022

Francesco Pellegrino, Giuseppe Falci, Elisabetta Paladino

Biblio References: 
arXiv preprint arXiv:2203.04017