  Graphene is known to be non-superconducting. However, surprising
superconductivity is recently discovered in a flat-band in a twisted bi-layer
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
non-vanishing superfluid density, and it realizes the long searched
superconducting states with non-vanishing center of mass momentum for Cooper
pairs.

Superconductivity