Superconducting proximity effect in $d$-wave cuprate/ graphene heterostructures

Superconducting proximity effects in graphene have received a great deal of attention for over a decade now. This has unveiled a plethora of exotic effects linked to the specificities of graphene's electronic properties. The vast majority of the related studies are based on conventional, low-temperature superconducting metals with isotropic $s$-wave pairing. Here we review recent advances made on the less studied case of unconventional high-temperature superconducting cuprates. These are characterized by an anisotropic $d$-wave pairing, whose interplay with Dirac electrons yields very rich physics and novel proximity behaviours. We provide a theoretical analysis and summarize the experiments reported so far. These unveil hints of proximity-induced unconventional pairing and demonstrate the gate-tunable, long-range propagation of high-temperature superconducting correlations in graphene. Finally, the fundamental and technological opportunities brought by the theoretical and experimental advances are discussed, together with the interest in extending similar studies to other Dirac materials.