Effects of SU(4) symmetry breaking on Andreev reflection in a graphene-superconductor junction in the quantum Hall regime

A quantum Hall (QH) edge state in proximity to a superconductor becomes a mixture of electron-like and hole-like states due Andreev processes. Such a state is called an Andreev edge state. In graphene valley and spin degeneracy lead to an approximate SU(4) symmetry that is reflected in the approximate 4-fold degeneracy of graphene's Landau levels (LLs). Interactions and the Zeeman effect break such approximate symmetry and the corresponding degeneracy of the LLs. In this talk, I will discuss the effects of SU(4) symmetry breaking terms on the transport properties of a graphene-superconductor junction when the graphene is in the QH regime. I will focus on the "n=1" and "n=0" LLs. For the n=0 LL I will show how the competition between interactions and Zeeman effect that lead to the canted antiferromagnetic phase affect the transport of the Andreev edge states.