1 Introduction 2 The electronic transport in graphene nanoribbons has opened up new challenges in nanoelectronics. A graphene nanoribbon (GNR) is a monolayer of carbon atoms arranged in a two-dimensional hon- eycomb lattice structure 1 − 4 and can be regarded as the basic building blocks for graphitic materials. Graphene based materials have potential applica- tions in several branch of nanoelectronics and due to their special electronic and physical properties they exhibit several novel properties like high car- rier mobility, 3 unconventional quantum Hall effect 5 and many others. The high carrier mobility in graphene demonstrates the idea for fabrication of high speed switching devices those have widespread applications in different fields. Recently GNRs are also used extensively in designing field-effect tran- sistors and this idea has been predicted in some re- cent nice papers. 6 − 8 It has many potential applica- tions and provides a huge interest in the community of nanoelectronics device research. Not only that, GNRs can be used to construct MOSFETs which perform much better than conventional Si MOS- FETs. In other experiment 9 it has been proposed that a narrow strip of graphene, the so-called a graphene nanoribbon, exhibits semiconducting be- havior due to its edge effects, unlike carbon nan- otubes of larger sizes which are mixtures of both metallic and semiconducting materials. The rea- son is that, in a narrow graphene sheet a band gap appears across the energy E = 0, while the gap gradually disappears with the increase of the size of the ribbon. It reveals a transformation from the semiconducting to the metallic material. This phe- nomenon has been studied in detail in a very recent theoretical work by the same author of this paper. 10 The situation becomes quite different for the case of honeycomb lattice ribbons with zigzag edges. Our study predicts that for a ribbon with zigzag edges always there exists an energy gap in the conduc- tance spectrum across the energy E = 0. The gap gradually decreases with the increase of the size of the ribbon (as expected), but it never vanishes even for much larger ribbons. This clearly reveals that a honeycomb lattice ribbon with zigzag edges al- ways exhibits the semiconducting behavior, unlike the lattice ribbons with armchair edges where both the semiconducting and the metallic phases are ob- served by tuning the size of a ribbon. All these edge effects in graphene ribbons provide many key informations in designing nanoelectronic devices. The aim of the present paper is to provide a qual- The paper is arranged in this way. Following the introduction (Section 1), in Section 2, we present the model and the theoretical formulations for our calculations. Section 3 discusses the significant re- Here we adopt a simple tight-binding model to describe the system and all the calculations are per- formed numerically. We narrate the conductance- energy and current-voltage characteristics as func- tions of the lengths and widths of ribbons. Our re- sults clearly predicts that a honeycomb lattice rib- bon with zigzag edges always shows the semicon- ducting nature irrespective of its length and width. In addition to these, several other factors of the Hamiltonian that describe a system also provide im- portant effects in the determination of the current across a bridge system. (iv) The dynamical fluctuation in the small-scale devices is another important factor which plays an active role and can be manifested through the mea- surement of shot noise , 32 − 33 a direct consequence of the quantization of charge. itative study of electron transport in honeycomb lattice ribbons with zigzag edges attached to two semi-infinite one-dimensional metallic electrodes (see Fig. 1). The theoretical description of elec- tron transport in a bridge system has been devel- oped based on the pioneering work of Aviram and Ratner. 11 Later, many significant experiments 12 − 13 have been done in several bridge systems to un- derstand the basic mechanisms underlying the electron transport. Though in literature many theoretical 14 − 25 as well as experimental papers 12 − 13 on electron transport are available, yet lot of con- troversies are still present between the theory and experiment even today. Several controlling factors are there which can regulate the electron transport in a conducting bridge significantly, and all these factors have to be taken into account properly to understand the transport mechanism. For our il- lustrative purposes, here we mention some of these issues. (i) The geometry of the conducting material be- tween the two electrodes itself is an important is- sue to control the electron transmission which has been described quite elaborately by Ernzerhof et al. 26 through some model calculations. (ii) The coupling of the bridging material to the electrodes significantly controls the current ampli- tude across any bridge system. 27 (iii) The quantum interference effect 27 − 31 of elec- tron waves passing through different arms of the bridging material becomes the most significant is- sue.