Triplet proximity effect and odd-frequency pairing in graphene

Abstract: We study the interplay between proximity-induced superconductivity and ferromagnetism in graphene by self-consistently solving the Bogoliubov-de Gennes equations on the honeycomb lattice. We find that a strong triplet proximity effect is generated in graphene, leading to odd-frequency pairing correlations. These odd-frequency correlations are clearly manifested in the local density of states of the graphene sheet, which can be probed via STM-measurements. Motivated by recent experiments on S$\mid$N$\mid$S graphene Josephson junctions, we also study the spectrum of Andreev-bound states formed in the normal region due to the proximity effect. Our results may be useful for interpreting spectroscopic data and can also serve as a guideline for future experiments.