Dirac boundary condition at the reconstructed zigzag edge of graphene

J. A. M. van Ostaay, A. R. Akhmerov, C. W. J. Beenakker, and M. Wimmer
Phys. Rev. B 84, 195434 – Published 8 November 2011

Abstract

Edge reconstruction modifies the electronic properties of finite graphene samples. We formulate a low-energy theory of the reconstructed zigzag edge by deriving the modified boundary condition to the Dirac equation. If the unit-cell size of the reconstructed edge is not a multiple of three with respect to the zigzag unit cell, valleys remain uncoupled and the edge reconstruction is accounted for by a single angular parameter ϑ. Dispersive edge states exist generically, unless |ϑ|=π/2. We compute ϑ from a microscopic model for the “reczag” reconstruction (conversion of two hexagons into a pentagon-heptagon pair), and show that it can be measured via the local density of states. In a magnetic field, there appear three distinct edge modes in the lowest Landau level, two of which are counterpropagating.

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  • Received 5 September 2011

DOI:https://doi.org/10.1103/PhysRevB.84.195434

©2011 American Physical Society

Authors & Affiliations

J. A. M. van Ostaay, A. R. Akhmerov, C. W. J. Beenakker, and M. Wimmer

  • Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, NL-2300 RA Leiden, The Netherlands

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Issue

Vol. 84, Iss. 19 — 15 November 2011

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