Boundary conditions for Dirac fermions on a terminated honeycomb lattice
Abstract
We derive the boundary condition for the Dirac equation corresponding to a tightbinding model on a twodimensional 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.
 Publication:

Physical Review B
 Pub Date:
 February 2008
 DOI:
 10.1103/PhysRevB.77.085423
 arXiv:
 arXiv:0710.2723
 Bibcode:
 2008PhRvB..77h5423A
 Keywords:

 73.21.Hb;
 73.22.Dj;
 73.22.f;
 73.63.Bd;
 Quantum wires;
 Single particle states;
 Electronic structure of nanoscale materials: clusters nanoparticles nanotubes and nanocrystals;
 Nanocrystalline materials;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 10 pages, 11 figures (v3, typos corrected, expanded Sec. III)