Dirac boundary condition at the reconstructed zigzag edge of graphene

Details Dirac boundary condition at the reconstructed zigzag edge of graphene Dirac boundary condition at the reconstructed zigzag edge of graphene

2011-09-05

arxiv.org/abs/1109.0884v3

Phys.Rev.B 84, 195434 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, 10 figures

Scientific paper

10.1103/PhysRevB.84.195434

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 $|\vartheta| = \pi/2$. 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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