Electronic transport properties

We numerically discuss the electronic transport properties of the disordered graphene nanoribbons. In general, electron scattering in a quantum wire is described by the scattering matrix [66]. Through the scattering matrix S, the amplitudes of the scattered waves O are related to the incident waves I,

. (19)

Here, r and r ⁰ are reflection matrices, t and t ⁰ are transmission matrices, L and R denote the left and right lead lines. The Landauer–Büttiker formula [73] relates the scattering matrix to the conductance of the sample. The electrical conductance is calculated using the Landauer–Büttiker formula,

Here the transmission matrix t (E) is calculated by means of the recursive Green function method [18, 74]. For simplicity, throughout this paper, we evaluate electronic conductance in units of quantum conductance (e ²/π h ¯), i.e. dimensionless conductance g (E). We would like to mention that recently the edge disorder effect on the electronic transport properties of graphene nanoribbons was studied using a similar approach [75]–[77].