Quantum dynamics of electron in graphene nanoribbons with edge disorder

Considering both the finite size and the edge disorder, we explore the dynamic behavior of electrons in graphene nanoribbons (GNRs) with various geometries in terms of quantum diffusion theory. It is shown that in the regime of stronger disorder, the decay exponent δ and the diffusion exponent β increase with increasing edge disorder, while they decrease in the regime of weaker disorder. This indicates that there exists a localization-quasi-delocalization transition in GNRs upon varying the strength of edge disorder, similar to that in a shell-doped nanowire. In addition, the edge disorder has an influence of varying importance on the electronic transport in GNR, which depends on its width and edge geometry, showing up as a singular quantum size effect. The results can contribute towards understanding of the strange transport properties of graphene sheets and their potential applications.