Edge States of Monolayer and Bilayer Graphene Nanoribbons

Abstract

On the basis of tight-binding lattice model, the edge states of monolayer and bilayer graphene nanoribbons (GNRs) with different edge terminations are studied. The effects of edge-hopping modulation, spin-orbital coupling (SOC), and bias voltage on bilayer GNRs are discussed. We observe the following: (i) Some new extra edge states can be created by edge-hopping modulation for monolayer GNRs. (ii) Intralayer Rashba SOC plays a role in depressing the band energy gap $E_g$ opened by intrinsic SOC for both monolayer and bilayer GNRs. An almost linear dependent relation, i.e., $E_g\sim {\lambda }_R$, is found. (iii) Although the bias voltage favors a bulk energy gap for bilayer graphene without intrinsic SOC, it tends to reduce the gap induced by intrinsic SOC. (iv) The topological phase of the quantum spin Hall effect can be destroyed completely by interlayer Rashba SOC for bilayer GNRs.

6 pages, 6 figures

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• Ferrimagnetic and antiferromagnetic phase in bilayer graphene nanoflake controlled with external electric fields
• Decay behavior of localized states at reconstructed armchair graphene edges
• A rigorous proof of non-existence of edge state in the semi-infinite armchair edged graphene
• Edge state in AB-stacked bilayer graphene and its correspondence with SSH ladder
• Study of edge states and conductivity in spin-orbit coupled bilayer graphene
• Edge states of graphene bilayer strip