  Using non-equilibrium Green's function formalism, we investigate nonlinear
transport and charging effects of gated graphene nanoribbons (GNRs) with even
number of zigzag chains. We find a negative differential resistance (NDR) over
a wide range of gate voltages with on/off ratio $\sim 10^6$ for narrow enough
ribbons. This NDR originates from the parity selection rule and also
prohibition of transport between discontinues energy bands. Since the external
field is well screened close to the contacts, the NDR is robust against the
electrostatic potential. However, for voltages higher than the NDR threshold,
due to charge transfer through the edges of ZGNR, screening is reduced such
that the external potential can penetrate inside the ribbon giving rise to
smaller values of off current. Furthermore, on/off ratio of the current depends
on the aspect ratio of the length/width and also edge impurity. Moreover,
on/off ratio displays a power law behavior as a function of ribbon length.
