  Electronic states in nanographite ribbons with zigzag edges are studied using
the extended Hubbard model with nearest neighbor Coulomb interactions. The
nearest Coulomb interactions stabilize electronic states with the opposite
electric charges separated and localized along both edges. Such states are
analogous as nanocondensers. Therefore, electric capacitance, defined using a
relation of polarizability, is calculated to examine nano functionalities. We
find that the behavior of the capacitance is widely different depending on
whether the system is in the magnetic or charge polarized phases. In the
magnetic phase, the capacitance is dominated by the presence of the edge states
while the ribbon width is small. As the ribbon becomes wider, the capacitance
remains with large magnitudes as the system develops into metallic zigzag
nanotubes. It is proportional to the inverse of the width, when the system
corresponds to the semiconducting nanotubes and the system is in the charge
polarized phase also. The latter behavior could be understood by the presence
of an energy gap for charge excitations.
