The effect of magnetic field and disorders on the electronic transport in graphene nanoribbons

We developed a unified mesoscopic transport model for graphene nanoribbons, which combines the non-equilibrium Green's function (NEGF) formalism with the real-space {\pi}-orbital model. Based on this model, we probe the spatial distributions of electrons under a magnetic field, in order to obtain insights into the various signature Hall effects in disordered armchair graphene nanoribbons (AGNR). In the presence of a uniform perpendicular magnetic field (B\perp-field), a perfect AGNR shows three distinct spatial current profiles at equilibrium, depending on its width. Under non-equilibrium conditions (i.e. in the presence of an applied bias), the net electron flow is restricted to the edges and occurs in opposite directions depending on whether the Fermi level lies within the valence or conduction band. For electrons at energy level below the conduction window, the B\perp-field gives rise to local electron flux circulation, although the global flux is zero. Our study also reveals the suppression of electron backscattering as a result of the edge transport which is induced by the B\perp-field. This phenomenon can potentially mitigate the undesired effects of disorders, such as the bulk and edge vacancies, on the transport properties of AGNR. Lastly, we show that the effect of B\perp-field on electronic transport is less significant in the multimode compared to the single mode electron transport.