Abstract
Using a tight-binding Bogoliubov--de Gennes formalism we show that nearest-neighbor spin-singlet (SB) correlations in graphene strongly enhance proximity effect and Josephson current in unconventional $d$-wave contact graphene Josephson junctions. We also establish a $1/(T\ensuremath{-}{T}_{c})$ functional dependence for the superconducting decay length, where ${T}_{c}$ is the superconducting transition temperature for the intrinsic SB correlations. We therefore propose that these junctions will provide a promising experimental system for measuring the effective strength of the intrinsic SB correlations in graphene.
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