Electric field control of spin-resolved edge states in graphene quantum   nanorings
  The electric-field effect on the electronic and magnetic properties of triangular and hexagonal graphene quantum rings with zigzag edge termination is investigated by means of the single-band tight-binding Hamiltonian and the mean-field Hubbard model. It is shown how the electron and spin states in the nanoring structures can be manipulated by applying an electric field. We find different spin-depolarization behaviors with variation of electric field strength due to the dependence of spin densities on the shapes and edges of this kind of nanorings. In the case of triangular quantum rings, the magnetization on the inner and outer edges can be selectively tuned and the spin states depolarize gradually as the field strength is increased, while in the case of hexagonal nanorings, the transverse electric field reduces the magnetic moments on both inner and outer edges symmetrically and rapidly. 
R. Farghadan and A. Saffarzadeh
cond-mat.mes-hall