  Electronic states in boron-nitride and boron-carbon-nitride nanoribbons with
zigzag edges are studied using the extended Hubbard model with nearest neighbor
Coulomb interactions. The charge and spin polarized states are considered, and
the phase diagram between two states is obtained. Next, the electric
capacitance is calculated in order to examine the nano-functionalities of the
system. Due to the presence of the strong site energies, the charge polarized
state overcomes the spin polarized states, giving the large difference of the
phase diagram in comparison with that of graphite system. The electronic
structures are always like of semiconductors. The capacitance calculated for
the charge polarized state with the realistic values of the Coulomb
interactions is inversely proportional to the ribbon width, owing to the
presence of the charge excitation energy gap.
