Geometric Inhibition of Superflow in Single-Layer Graphene Suggests a Staggered-Flux Superconductivity in Bilayer and Trilayer Graphene

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