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 $\mu \left(n\right)\sim n^{-\lambda }$, with $0\le \lambda \lesssim 0.5$. 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, quasiballistic, or diffusive). Based on our findings we discuss available experimental results.

• Received 28 August 2009

DOI:https://doi.org/10.1103/PhysRevB.80.245432