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Nonlinear Transport through ultra-narrow Zigzag Graphene Nanoribbons: non-equilibrium charge and bond currents

The electronic nonlinear transport through ultra narrow graphene nanoribbons (sub-$10nm$) is studied. A stable region of negative differential resistance (NDR) appears in the I-V characteristic curve of {\it odd} zigzag graphene nanoribbons (ZGNRs) in both positive and negative polarity. This NDR originates from a transport gap inducing by a selection rule which blocks electron transition between disconnecting energy bands of ZGNR. Based on this transition rule, on/off ratio of the current increases exponentially with the ribbon length up to $10^5$. In addition, charging effects and also spatial distribution of bond currents was studied by using non-equilibrium Green's function formalism in the presence of e-e interaction at a mean field level. On the other hand, we also performed an {\it ab initio} density functional theory calculation of transmission through a passivated graphene nanoribbon to demonstrate robustness of the transport gap against hydrogen termination of the zigzag edges.