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arXiv · 0710.2723

Boundary conditions for Dirac fermions on a terminated honeycomb lattice

A. R. Akhmerov·C. W. J. Beenakker
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Abstract

We derive the boundary condition for the Dirac equation corresponding to a tight-binding model on a two-dimensional honeycomb lattice terminated along an arbitary direction. Zigzag boundary conditions result generically once the boundary is not parallel to the bonds. Since a honeycomb strip with zigzag edges is gapless, this implies that confinement by lattice termination does not in general produce an insulating nanoribbon. We consider the opening of a gap in a graphene nanoribbon by a staggered potential at the edge and derive the corresponding boundary condition for the Dirac equation. We analyze the edge states in a nanoribbon for arbitrary boundary conditions and identify a class of propagating edge states that complement the known localized edge states at a zigzag boundary.

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A. R. Akhmerov, C. W. J. Beenakker. 2008-01-11. Boundary conditions for Dirac fermions on a terminated honeycomb lattice. https://doi.org/10.1103/physrevb.77.085423

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