title: Evolution of Landau levels into edge states in graphene.
abstract: Two-dimensional electron systems in the presence of a magnetic field support topologically ordered states, in which the coexistence of an insulating bulk with conducting one-dimensional chiral edge states gives rise to the quantum Hall effect. For systems confined by sharp boundaries, theory predicts a unique edge-bulk correspondence, which is central to proposals of quantum Hall-based topological qubits. However, in conventional semiconductor-based two-dimensional electron systems, these elegant concepts are difficult to realize, because edge-state reconstruction due to soft boundaries destroys the edge-bulk correspondence. Here we use scanning tunnelling microscopy and spectroscopy to follow the spatial evolution of electronic (Landau) levels towards an edge of graphene supported above a graphite substrate. We observe no edge-state reconstruction, in agreement with calculations based on an atomically sharp boundary. Our results single out graphene as a system where the edge structure can be controlled and the edge-bulk correspondence is preserved.
authors.affiliation: Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855, USA.
authors.forename: Guohong
authors.initials: G
authors.lastname: Li
authors.forename: Adina
authors.initials: A
authors.lastname: Luican-Mayer
authors.forename: Dmitry
authors.initials: D
authors.lastname: Abanin
authors.forename: Leonid
authors.initials: L
authors.lastname: Levitov
authors.forename: Eva Y
authors.initials: EY
authors.lastname: Andrei