  The effect of electron-electron interaction on the electronic structure of
Aharonov-Bohm (AB) graphene quantum rings (GQRs) is explored theoretically
using the single-band tight-binding Hamiltonian and the mean-field Hubbard
model. The electronic states and magnetic properties of hexagonal, triangular
and circular GQRs with different sizes and zigzag edge terminations are
studied. The results show that, although the AB oscillations in the all types
of nanoring are affected by the interaction, the spin splitting in the AB
oscillations strongly depends on the geometry and the size of graphene
nanorings. We found that the total spin of hexagonal and circular rings is zero
and therefore, no spin splitting can be observed in the AB oscillations.
However, the non-zero magnetization of the triangular rings breaks the
degeneracy between spin-up and spin-down electrons, which produces
spin-polarized AB oscillations.
