Topological Insulator in the Core of the Superconducting Vortex in Graphene

The core of the vortex in a general superconducting order parameter in graphene is argued to be ordered, with the possible local order parameters forming the algebra U(1) x Cl(3). A sufficiently strong Zeeman coupling of the magnetic field of the vortex to the electron spin breaks the degeneracy in the core in favor of the anomalous quantum Hall state. I consider a variety of superconducting condensates on the honeycomb lattice and demonstrate the surprising universality of this result. A way to experimentally determine the outcome of the possible competition between different types of orders in the core is proposed.