SU(4) symmetry breaking and Andreev edge states in quantum Hall graphene-superconductor junctions

A quantum Hall (QH) edge state in proximity to a superconductor becomes a mixture of electron-like and hole-like states due to 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 (LL). Interactions and the Zeeman effect break such approximate symmetry and the corresponding degeneracy of the LLs. We present the effects of SU(4) symmetry breaking using a simple low-energy model for Andreev edge states. For the N=0 graphene LL we study how the competition between interactions and Zeeman effect that lead to the canted antiferromagnetic phase affect the transport of the Andreev edge states. For the N=1 LL we investigate how Zeeman and valley splitting may be used to modulate Andreev edge state interference patterns.