Edge states and the quantized Hall effect in graphene

By L. Brey, H. Fertig. 2006

208 citations recorded by the source corpus.

We study edges states of graphene ribbons in the quantized Hall regime, and show that they can be described within a continuum model (the Dirac equation) when appropriate boundary conditions are adopted. The two simplest terminations, zigzag and armchair edges, are studied in detail. For zigzag edges, we find that the lowest Landau level states terminate in two types of edge states, dispersionless and current-carrying surface states. The latter involve components on different sublattices that may be separated by distances far greater than the magnetic length. For armchair edges, the boundary conditions are met by admixing states from different valleys, and we show that this leads to a single set of edges states for the lowest Landau level and two sets for all higher Landau levels. In both cases, the resulting Hall conductance step for the lowest Landau level is half that between higher Landau levels, as observed in experiment.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/bc268e72757018534ee7119a870b51ba3a11bdb8

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

The electronic properties of graphene (2007, methodology): “The wavefun tions in the dis rete latti e must be real,and at large distan es the a tual solution found neara va an y tends to a superposition of two solutionsformed from wavefun tions from the two valleys withequal weight, in a way similar to the mixing at arm hairedges (Brey and Fertig, 2006b).”
Electronic properties of graphene in a strong magnetic field (2010, result): “…is a simplification to treat the graphene edges in the continuum description of the Dirac equation, a more sophisticated treatment that takes into account the geometry of the edges yields, apart from a fine structure of the levels at the edge, qualitatively similar results (Brey and Fertig, 2006).”