Sublattice polarization and filamentary superconductivity in strained graphene

Periodic strain engineering in monolayer graphene provides a versatile platform to generate colossal pseudo-magnetic fields and flat pseudo-Landau levels directly in a single atomic sheet. While the electronic topology and transport properties of the normal state in these systems have been extensively studied, the superconducting ground state in such strain-modulated landscapes remains an unexplored frontier. In this work, we investigate the superconducting phase of periodically corrugated graphene using a self-consistent Bogoliubov-de Gennes framework. We find that, contrary to the conventional expectation that a high density of states universally enhances pairing, the macroscopic superconducting coherence is significantly hindered in the flat-band regions. This limitation originates from strain-induced sublattice polarization, where the zero-energy electronic states are spatially segregated between the $A$ and $B$ sublattices. Such spatial disjointedness hampers the inter-sublattice coherence required for a robust pairing instability, effectively decoupling the high-density flat-band states from the superconducting condensate. Consequently, as the pairing interaction increases, the system undergoes a striking spatial crossover: superconductivity sharply relocates from the flat-band regions to emerge as robust, quasi-one-dimensional filaments at the geometric nodes where local sublattice symmetry is restored. Our findings reveal that the spatial distribution of wavefunctions, governed by sublattice degrees of freedom, is a decisive factor in determining the superconducting properties of strain-engineered Dirac materials.