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arXiv · 1109.0884

Dirac boundary condition at the reconstructed zigzag edge of graphene

J. A. M. van Ostaay·A. R. Akhmerov·C. W. J. Beenakker·M. Wimmer
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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 $\vartheta$. Dispersive edge states exist generically, unless $|\vartheta| = π/2$. We compute $\vartheta$ 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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J. A. M. van Ostaay, A. R. Akhmerov, C. W. J. Beenakker, M. Wimmer. 2011-10-26. Dirac boundary condition at the reconstructed zigzag edge of graphene. https://doi.org/10.1103/physrevb.84.195434

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