in many theoretical as well as experimental papers in the literature. The key feature observed from these I - V characteristics is that for all such ribbons the electron starts to conduct beyond some finite bias voltage, the so-called threshold bias voltage V$_{th}$ , and it decreases very slowly with the change of the size of the ribbon. Our study reveals that the threshold bias voltage never drops to zero, even for much larger systems, and accordingly, we can pre- dict that a honeycomb lattice ribbon with zigzag edges exhibits only the semiconducting behavior. 4 Concluding remarks References is a major challenge to us, since over the last few years people have studied a lot to incorporate this effect, but no such proper theory has yet been devel- oped. In this work, we have presented all the results only for the ordered systems. But in real samples, the presence of impurities will affect the electronic structure and hence the transport properties. Be- side these, in experiments, the graphene nanoribbon is deposited on an insulating substrate which has also not been included in our present study, and, it has been observed from first-principles calcula- tions that the effect of the substrate is too week. 37 The effect of the temperature has already been pointed out earlier, and, it has been examined that the presented results will not change significantly even at finite temperature, since the broadening of the energy levels of the ribbon due to its coupling with the electrodes will be much larger than that of the thermal broadening. 34 The other important assumption is that here we have chosen the linear chains instead of wider leads, since we are mainly interested about the basic physics of the ribbon. Though the results presented here change with the increase of the thickness of the leads, but all the ba- sic features remain quite invariant. The effect of the boundary is also an important issue in this context. Here we have considered only the perfect geometry of the nannoribbons. Several interesting features will be observed for the nanoconstrictions with dif- ferent shapes 38 like, square-shaped, wedge-shaped nanoconstrictions, etc. Finally, we would like to say that we need further study in such systems by incorporating all these effects. To summarize, we have addressed electron trans- port properties in honeycomb lattice ribbons with zigzag edges attached to two semi-infinite one- dimensional metallic electrodes within the tight- binding framework. We have numerically computed the conductance-energy and current-voltage charac- teristics concerning the dependence on the lengths and widths of the ribbons. The results have pre- dicted that for such ribbons i.e., ribbons with zigzag edges a central energy gap always exists across the energy E = 0 in the conductance spectrum. The gap decreases gradually with the increase of the size of the ribbon but it never vanishes. This phe- nomenon clearly manifests that a honeycomb lat- tice ribbon with zigzag edges always shows semi- conducting nature, unlike the lattice ribbons with armchair edges where both the semiconducting and the metallic phases are observed by controlling the size of the ribbon. This semiconducting behavior of the lattice ribbons with zigzag edges has been much more clearly addressed from our presented current- voltage characteristics. It has been observed that the current starts to appear beyond some finite bias voltage i.e., the threshold bias voltage V$_{th}$ has a non-zero value. This V$_{th}$ doesn’t change apprecia- bly with the increase of the size of the ribbon and we have also examined that the threshold bias voltage never reduces to zero even for much larger systems, which predicts the semiconducting nature only. This is our first step to describe how the elec- tron transport properties in honeycomb lattice rib- bons with zigzag edges depends on the size of the ribbons. We have made several realistic assump- tions by ignoring the effects of the electron-electron correlation, disorder, interaction with a substrate, temperature, finite width of the electrodes, bound- ary of the ribbons, etc. Here we discuss very briefly about these approximations. The inclusion of the electron-electron correlation in the present model 7 [1] V. V. Cheianov, V. Fal’ko, and B. L. Altshuler, Science 315, 1252 ( 2007 ). [2] J. B. Pendry, Science 315, 1226 ( 2007 ). [3] A. K. Geim and K. S. Novoselov, Nat. Mater. 6, 183 ( 2007 ). [4] C. Berger, Z. Song, X. Li, X. Wu, N. Brown, C. Naud, D. Mayou, T. Li, J. Hass, A. N. Marchenkov, E. H. Corrad, P. N. First, and W. A. de Heer, Science 312, 1191 ( 2006 ). [5] Y. Zhang, Y. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 ( 2005 ). [6] Y. Ouyang, Y. Yoon, J. K. Fodor, and J. Guo, Appl. Phys. Lett. 89, 203107 ( 2006 ).