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.