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Transition from ballistic to diffusive behavior of graphene ribbons in the presence of warping and charged impurities

We study the effects of the long-range disorder potential and warping on the conductivity and mobility of graphene ribbons using the Landauer formalism and the tight-binding p-orbital Hamiltonian. We demonstrate that as the length of the structure increases the system undergoes a transition from the ballistic to the diffusive regime. This is reflected in the calculated electron density dependencies of the conductivity and the mobility. In particular, we show that the mobility of graphene ribbons varies as mu(n) n^(-lambda), with 0<lambda<0.5. The exponent lambda depends on the length of the system with lambda=0.5 corresponding to short structures in the ballistic regime, whereas the diffusive regime lambda=0 (when the mobility is independent on the electron density) is reached for sufficiently long structures. Our results can be used for the interpretation of experimental data when the value of lambda can be used to distinguish the transport regime of the system (i.e. ballistic, quasi-ballistic or diffusive). Based on our findings we discuss available experimental results.