SO(5) symmetry in the quantum Hall effect in graphene

Electrons in graphene have four flavors associated with low-energy spin and valley degrees of freedom. The fractional quantum Hall effect in graphene is dominated by long-range Coulomb interactions, which are invariant under rotations in spin-valley space. This SU(4) symmetry is spontaneously broken at most filling factors, and also weakly broken by atomic scale valley-dependent and valley-exchange interactions with coupling constants g(z) and g(perpendicular to?). In this paper, we demonstrate that when g(z) = -g(perpendicular to?), an exact SO(5) symmetry survives which unifies the Neel spin order parameter of the antiferromagnetic state and the XY valley order parameter of the Kekule distortion state into a single five-component order parameter. The proximity of the highly insulating quantum Hall state observed in graphene at nu = 0 to an ideal SO(5) symmetric quantum Hall state remains an open experimental question. We illustrate the physics associated with this SO(5) symmetry by studying the multiplet structure and collective dynamics of filling factor nu = 0 quantum Hall states based on exact-diagonalization and low-energy effective theory approaches. This allows to illustrate how manifestations of the SO(5) symmetry would survive even when it is weakly broken.