Band-Selective Filter in a Zigzag Graphene Nanoribbon

Electric transport of a zigzag graphene nanoribbon through a step-like potential or a barrier potential is investigated by using the recursive Green's function method. In the case of the step-like potential, we demonstrate numerically that scattering processes obey a selection rule for the band indices when the number of zigzag chains is even; the electrons belonging to the ``even'' (``odd'') bands are scattered only into the even (odd) bands so that the parity of wavefunctions is preserved. The so-called valley-valve effect can be explained by this selection rule. In the case of the barrier potential, by tuning the barrier height to be an appropriate value, we show that it can work as the ``band-selective filter'', which transmits electrons selectively with respect to the indices of the bands to which the incident electrons belong. Finally, we suggest that this selection rule can be observed in the conductance by applying two barrier potentials.