Edge states of bilayer graphene in the quantum Hall regime

We study the low-energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundary geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge-state behaviors: weakly, strongly, and nondispersive edge states. These three behaviors may all be understood within a continuum model, and related by nonlinear transformations to the spectra of quantum Hall edge states in a conventional two-dimensional electron system. In all cases, the edge states closest to zero energy include a holelike edge state of one valley and a particlelike state of the other on the same edge, which may or may not cross, depending on the boundary condition. Edge states with the same spin generically have anticrossings that complicate the spectra, but which may be understood within degenerate perturbation theory. The results demonstrate that the number of edge states crossing the Fermi level in clean, undoped bilayer graphene depends both on boundary conditions and the energies of the bulk states.