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We study the effects of the long-range disorder potential and warping on theconductivity and mobility of graphene ribbons using the Landauer formalism andthe tight-binding p-orbital Hamiltonian. We demonstrate that as the length ofthe structure increases the system undergoes a transition from the ballistic tothe diffusive regime. This is reflected in the calculated electron densitydependencies of the conductivity and the mobility. In particular, we show thatthe mobility of graphene ribbons varies as mu(n) n^(-lambda), with0<lambda<0.5. The exponent lambda depends on the length of the system withlambda=0.5 corresponding to short structures in the ballistic regime, whereasthe diffusive regime lambda=0 (when the mobility is independent on the electrondensity) is reached for sufficiently long structures. Our results can be usedfor the interpretation of experimental data when the value of lambda can beused to distinguish the transport regime of the system (i.e. ballistic,quasi-ballistic or diffusive). Based on our findings we discuss availableexperimental results.

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