Localized states at zigzag edges of bilayer graphene

TL;DR

This paper discovers and analytically characterizes zero energy localized surface states at zigzag edges of bilayer graphene, revealing two distinct families with different layer localizations and exploring their behavior under various conditions.

Contribution

It provides the first analytic solutions for these edge states and classifies them into two families based on their layer localization and penetration depth.

Findings

Zero energy surface states exist at zigzag edges of bilayer graphene.

Surface states can be confined to a single layer or extend over both layers.

Electronic structure varies with bias voltage and edge configuration.

Abstract

We report the existence of zero energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wavefunctions of these peculiar surface states. It is shown that zero energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene; (ii) states with finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.