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 and cleanest monolayer graphene remains a big puzzle. Here, through realistic computation of electronic structure, we identify a systematic trend that superconductivity appears to emerge only upon alteration of the low-energy electronic lattice from the underlying honeycomb atomic structure. We then demonstrate that the same inhibition of superfluidity is reproduced naturally in an emergent Bose liquid (EBL) as a quantum Bose metal resulting from geometric frustration of the bosonic bond lattice that disables quantum phase coherence. In comparison, upon deviating from the honeycomb lattice, relief of geometric frustration allows robust superfluidity with non-trivial spatial structure. For the specific examples of bi-layer and tri-layer graphene under external electric field, an EBL would develop superfluidity with staggered-flux that breaks the time reversal symmetry. Our study also suggests possible realization of the long-sought superconductivity in single-layer graphene via application of uni-directional strain.