Strain-induced time-reversal odd superconductivity in graphene

Time-reversal symmetry breaking superconductors are exotic phases of matter with fascinating properties, which are, however, encountered rather sparsely. Here we identify the possibility of realizing such a superconducting ground state that exhibits an $f+is$ pairing symmetry in strained graphene. Although the underlying attractive interactions need to be sufficiently strong and comparable in pristine graphene to support such pairing state, we argue that strain can be conducive for its formation even for weak interactions. We show that quantum-critical behavior near the transition is controlled by a multicritical point, characterized by various critical exponents computed here in the framework of an $\epsilon$-expansion near four spacetime dimensions. Furthermore, a vortex in this mixed superconducting state hosts a pair of Majorana fermions supporting a quartet of insulating and superconducting orders, among which topologically nontrivial quantum spin Hall insulator. These findings suggest that strained graphene could provide a platform for the realization of exotic superconducting states of Dirac fermions.