Edge disorder and localization regimes in bilayer graphene nanoribbons

TL;DR

This study investigates the electronic properties of bilayer graphene nanoribbons, focusing on edge disorder effects, conductance quantization, and localization regimes, revealing differences from monolayer ribbons and the impact of width and disorder.

Contribution

It provides a theoretical analysis of magnetoelectronic properties and edge disorder effects in bilayer graphene nanoribbons, highlighting differences from monolayer systems and the influence on transport gaps and localization.

Findings

Conductance quantization differs for zigzag and armchair edges.

Edge disorder induces a transport gap around the neutrality point.

Localization length behavior varies inside and outside the transport gap.

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 quantized as 2(n+1)G_ for the zigzag edges and nG_0 for the armchair edges with G_{0}=2e^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 in bilayer and monolayer nanoribbons. While for the GNRs E_{g}^{GNR}is proportional to 1/W, the corresponding transport gap E_{g}^{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, 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 \xi grows rapidly as the Fermi energy increases and becomes very similar for BGNs and GNRs.