Interplay between valley polarization and electron-electron interaction in a graphene ring

We have studied the interplay of valley polarization and the Coulomb interaction on the energy spectrum, persistent current, and optical absorption of a graphene quantum ring. We show that the interaction has a dramatic effect on the nature of the ground state as a function of the magnetic flux and that the absence of exchange interaction between electrons in opposite valleys means that the singlet-triplet degeneracy is not lifted for certain few-electron states. The additional energy-level crossings (fractional flux periodicity) due to the interaction directly lead to extra steps in the persistent current and intricate structures in the absorption spectrum that should be experimentally observable. By varying the width of the ring, the nature of the ground state at zero field can be varied and this is manifest in the measurable properties we discuss.