Abstract

Grain boundaries and defect lines in graphene are intensively studied for their novel electronic and magnetic properties. However, there is not a complete comprehension of the appearance of localized states along these defects. Graphene grain boundaries are herein seen as the outcome of matching two semi-infinite graphene sheets with different edges. We classify the energy spectra of grain boundaries into three different types, directly related to the combination of the four basic classes of spectra of graphene edges. From the specific geometry of the grains, we are able to obtain the band structure and the number of localized states close to the Fermi energy. This provides a new understanding of states localized at grain boundaries, showing that they are derived from the edge states of graphene. Such knowledge is crucial for the ultimate tailoring of electronic and optoelectronic applications.

Highlights

  • Grown graphene presents grain boundaries which have been clearly observed by several techniques, for example, high-resolution transmission electron microscopy [1, 2]

  • We are bringing into contact these ideas about localized states in graphene edges to give a more comprehensive explanation of states appearing in extended defect lines in graphene

  • (i) We present a theory of localized states around the Fermi energy (EF) in intrinsic graphene due to the grain boundaries built of pentagon/heptagon (5–7) defects, which are equivalent to defect lines at junctions between two graphene sheets

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Summary

Introduction

Grown graphene presents grain boundaries which have been clearly observed by several techniques, for example, high-resolution transmission electron microscopy [1, 2]. As a matter of fact, grain boundaries present localized states, which have been proven to be crucial, with distinct electronic [9, 10], magnetic [11] and mechanical [12] properties that depend on the atomic line junctions. These localized states allow for the decoration of line defects with adsorbates [6, 13], which opens a novel route for nanosensor applications. Our approach offers a new insight on the origin of these localized states, and allows for the prediction of their electronic characteristics without performing numerical calculations

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