Spin and electronic correlations in gated graphene quantum rings

We present a theory of graphene quantum rings designed to produce degenerate shells of single-particle states close to the Fermi level. We show that populating these shells with carriers using a gate leads to correlated ground states with finite total electronic spin. Using a combination of tight-binding and configuration-interaction methods, we predict the ground state and the total spin of the system as a function of the filling of the shell. We show that for smaller quantum rings, the spin polarization of the ground state at half filling depends strongly on the size of the system but reaches a maximum value beyond a critical size.