Boundary conditions for Dirac fermions on a terminated honeycomb lattice

Details Boundary conditions for Dirac fermions on a terminated honeycomb lattice Boundary conditions for Dirac fermions on a terminated honeycomb lattice

2007-10-15

arxiv.org/abs/0710.2723v3

Phys.Rev.B 77, 085423 (2008)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

10 pages, 11 figures (v3, typos corrected, expanded Sec. III)

Scientific paper

10.1103/PhysRevB.77.085423

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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