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In great contrast to the numerous discoveries of superconductivity inlayer-stacked graphene systems, the absence of superconductivity in thesimplest and cleanest monolayer graphene remains a big puzzle. Here, throughrealistic computation of electronic structure, we identify a systematic trendthat superconductivity appears to emerge only upon alteration of the low-energyelectronic lattice from the underlying honeycomb atomic structure. We thendemonstrate that this inhibition can result from from geometric frustration ofthe bond lattice that disables quantum phase coherence of the order parameterresiding on it. In comparison, upon deviating from the honeycomb lattice,relief of geometric frustration allows robust superfluidity with non-trivialspatial structure. For the specific examples of bilayer and trilayer grapheneunder an external electric field, such bond centered order parameter woulddevelop superfluidity with staggered flux that breaks the time-reversalsymmetry. Our study also suggests the possible realization of the long-soughtsuperconductivity in single-layer graphene via the application ofuni-directional strain.

Geometric inhibition of superflow in single-layer graphene suggests a staggered-flux superconductivity in bilayer and trilayer graphene