  While not widely recognized, electronic correlations might play an important
role in graphene. Indeed, Pauling's resonance valence bond (RVB) theory for the
pp-bonded planar organic molecules, of which graphene is the infinite
extension, already established the importance of the nearest neighbor
spin-singlet bond (SB) state in these materials. However, despite the recent
growth of interest in graphene, there is still no quantitative estimate of the
effects of Coulomb repulsion in either undoped or doped graphene. Here we use a
tight-binding Bogoliubov-de Gennes (TB BdG) formalism to show that in
unconventional d-wave contact graphene Josephson junctions the intrinsic SB
correlations are strongly enhanced. We show on a striking effect of the SB
correlations in both proximity effect and Josephson current as well as
establishing a 1/(T-T_c) functional dependence for the superconducting decay
length. Here T_c is the superconducting transition temperature for the
intrinsic SB correlations, which depends on both the effects of Coulomb
repulsion and the doping level. We therefore propose that d-wave contact
graphene Josephson junctions will provide a promising experimental system for
the measurement of the effective strength of intrinsic SB correlations in
graphene.
