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Graphene is known to be non-superconducting. However, surprisingsuperconductivity is recently discovered in a flat-band in a twisted bi-layergraphene. Here we show that superconductivity can be more easily realized intopological flat-bands induced by strain in graphene through periodic ripples.Specifically, it is shown that by including correlation effects, the chirald-wave superconductivity can be stabilized under strain even for slightly dopedgraphene. The chiral d-wave superconductivity generally coexists with chargedensity waves (CDW) and pair density waves (PDW) of the same period.Remarkably, a pure PDW state with doubled period that coexists with the CDWstate is found to emerge at a finite temperature region under reasonable strainstrength. The emergent PDW state is shown to be superconducting withnon-vanishing superfluid density, and it realizes the long searchedsuperconducting states with non-vanishing center of mass momentum for Cooperpairs.

Strain induced superconducting pair-density-wave states in graphene