Quantum valley Hall effect in proximity-induced superconducting graphene: An experimental window for deconfined quantum criticality

We show that when superconductivity is induced in graphene through proximity effect, a superconducting vortex is dressed with an interesting pattern of textured order parameters. Furthermore, passing a supercurrent in a superconducting graphene sample induces accumulation of valley pseudospin quantum number at edges: the quantum valley Hall effect will be observable in superconducting graphene. These effects reveal a quantum duality between different order parameters that is at heart of the Wess-Zumino-Witten term.