Strain-induced superconducting pair density wave states in graphene

Graphene is known to be nonsuperconducting. However, surprising superconductivity is recently discovered in a flat band in a twisted bilayer graphene. Here, we show that superconductivity can be more easily realized in topological flat bands induced by strain in graphene through periodic ripples. Specifically, it is shown that by including correlation effects, the chiral d-wave superconductivity can be stabilized under strain even for slightly doped graphene. The chiral d-wave superconductivity generally coexists with charge density waves (CDW) and pair density waves (PDW) of the same period. Remarkably, a pure PDW state with doubled period that coexists with the CDW state is found to emerge at a finite-temperature region under reasonable strain strength. The emergent PDW state is shown to be superconducting with nonvanishing superfluid density, and it realizes the long-sought-after superconducting states with nonvanishing center-of-mass momentum for Cooper pairs.