Edge disorder and localization regimes in bilayer graphene nanoribbons

Abstract

A theoretical study of the magnetoelectronic properties of zigzag and armchair bilayer graphene nanoribbons (BGNs) is presented. Using the recursive Green's function method, we study the band structure of BGNs in uniform perpendicular magnetic fields and discuss the zero-temperature conductance for the corresponding clean systems. The conductance is quantized as $2(n+1){G}_{0}$ for the zigzag edges and $n{G}_{0}$ for the armchair edges with ${G}_{0}=2{e}^{2}/h$ being the conductance unit and $n$ an integer. Special attention is paid to the effects of edge disorder. As in the case of monolayer graphene nanoribbons (GNR), a small degree of edge disorder is already sufficient to induce a transport gap around the neutrality point. We further perform comparative studies of the transport gap ${E}_{g}$ and the localization length $\ensuremath{\xi}$ in bilayer and monolayer nanoribbons. While for the GNRs ${E}_{g}^{\text{GNR}}\ensuremath{\sim}1/W$, the corresponding transport gap ${E}_{g}^{\text{BGN}}$ for the bilayer ribbons shows a more rapid decrease as the ribbon width $W$ is increased. We also demonstrate that the evolution of localization lengths with the Fermi energy shows two distinct regimes. Inside the transport gap, $\ensuremath{\xi}$ is essentially independent on energy and the states in the BGNs are significantly less localized than those in the corresponding GNRs. Outside the transport gap $\ensuremath{\xi}$ grows rapidly as the Fermi energy increases and becomes very similar for BGNs and GNRs.