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In graphene, the approximate SU(4) symmetry associated with the spin andvalley degrees of freedom in the quantum Hall (QH) regime is reflected in the4-fold degeneracy of graphene's Landau levels (LL's). Interactions and theZeeman effect break such approximate symmetry and lift the correspondingdegeneracy of the LLs. We study how the breaking of the approximate SU(4)symmetry affects the properties of graphene's QH edge modes located inproximity to a superconductor. We show how the lifting of the 4-fold degeneracyqualitatively modifies the transport properties of the QH-superconductorheterojunction. For the zero LL, by placing the edge modes in proximity to asuperconductor, it is in principle possible to realize a 1D topologicalsuperconductor supporting Majoranas in the presence of sufficiently strongZeeman field. We estimate the topological gap of such a topologicalsuperconductor and relate it to the properties of the QH-superconductorinterface.

SU(4) Symmetry Breaking and Induced Superconductivity in Graphene Quantum Hall Edges