Year: 2008
Type: article
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 arbitrary 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.
Source: Physical Review B
Authors: A. R. Akhmerov, C. W. J. Beenakker
Institution: Leiden University
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2035533039