Geometric Inhibition\nof Superflow in Single-Layer\nGraphene Suggests a Staggered-Flux Superconductivity in Bilayer and\nTrilayer Graphene

In\ngreat contrast to the numerous discoveries of superconductivity\nin layer-stacked graphene systems, the absence of superconductivity\nin the simplest monolayer graphene remains quite puzzling. Here, through\nrealistic computation of the electronic structure, we identify a systematic\ntrend that superconductivity emerges only upon alteration of the low-energy\nelectronic lattice from the underlying honeycomb atomic structure.\nWe then demonstrate that this inhibition can result from geometric\nfrustration of the bond lattice that disables the quantum phase coherence\nof the order parameter residing on it. In comparison, upon deviation\nfrom the honeycomb lattice, relief of geometric frustration allows\nrobust superfluidity with nontrivial spatial structures. For the specific\nexamples of bilayer and trilayer graphene under an external electric\nfield, such a bond-centered order parameter would develop superfluidity\nwith staggered flux that breaks the time-reversal symmetry. Our study\nalso suggests the possible realization of the long-sought superconductivity\nin single-layer graphene via the application of unidirectional strain.