Edge States of Bilayer Graphene in the Quantum Hall Regime

Abstract

We study the low energy edge states of bilayer graphene in a strong perpendicular magnetic field. Several possible simple boundaries geometries related to zigzag edges are considered. Tight-binding calculations reveal three types of edge state behaviors: weakly, strongly, and non-dispersive edge states. These three behaviors may all be understood within a continuum model, and related by non-linear 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 hole-like edge state of one valley and a particle-like 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.

12 pages, 6 figures

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• Electronic structure and layer-resolved transmission of bilayer graphene nanoribbon in the presence of vertical fields
• Quantum phase transition in a multicomponent anyonic Lieb-Liniger model
• Valley-kink in Bilayer Graphene at $\nu =0$: A Charge Density Signature for Quantum Hall Ferromagnetism
• Spontaneous Layer Polarization and Conducting Domain Walls in the Quantum Hall Regime of Bilayer Graphene
• Superfluid-Insulator transition of quantum Hall domain walls in bilayer graphene
• Edge state in AB-stacked bilayer graphene and its correspondence with SSH ladder
• Collective Edge Modes of a Quantum Hall Ferromagnet in Graphene
• Helical quantum Hall Edge modes in bilayer graphene: a realization of quantum spin-ladders
• Edge states in bilayer graphene in a magnetic field