  We consider superconducting properties of a two-dimensional Dirac material
such as graphene under strain that produces a flat band spectrum in the normal
state. We show that in the superconducting state, such a model results in a
highly increased critical temperature compared to the case without the strain,
inhomogenous order parameter with two-peak shaped local density of states and
yet a large and almost uniform and isotropic supercurrent. This model could be
realized in strained graphene or ultracold atom systems and could be
responsible for unusually strong superconductivity observed in some graphite
interfaces and certain IV-VI semiconductor heterostructures.
