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      Edge states in bilayer graphene in a magnetic field

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          Abstract

          Edge states in biased bilayer graphene in a magnetic field are studied within the four-band continuum model. The analysis is done for the semi-infinite graphene plane and for the graphene ribbon of a finite width, in the cases of zigzag and armchair edges. Exact dispersion equations for the edge states and analytic expressions for their wave functions are written in terms of the parabolic cylinder functions. The spectrum of edge states for each type of the boundary conditions is found by numerically solving the corresponding dispersion equations. The low-energy modes localized at zigzag edges are explored in detail.

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          Edge state in graphene ribbons: Nanometer size effect and edge shape dependence

          Kyoko Nakada, Mitsutaka Fujita, Gene F Dresselhaus … (1996)
          Article 0 comments Cited 1070 times – based on 0 reviews     Review now
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            Electronic States of Graphene Nanoribbons

            Luis Brey, H. Fertig (2006)
            We study the electronic states of narrow graphene ribbons (``nanoribbons'') with zigzag and armchair edges. The finite width of these systems breaks the spectrum into an infinite set of bands, which we demonstrate can be quantitatively understood using the Dirac equation with appropriate boundary conditions. For the zigzag nanoribbon we demonstrate that the boundary condition allows a particle- and a hole-like band with evanescent wavefunctions confined to the surfaces, which continuously turn into the well-known zero energy surface states as the width gets large. For armchair edges, we show that the boundary condition leads to admixing of valley states, and the band structure is metallic when the width of the sample in lattice constant units is divisible by 3, and insulating otherwise. A comparison of the wavefunctions and energies from tight-binding calculations and solutions of the Dirac equations yields quantitative agreement for all but the narrowest ribbons.
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              Coulomb-driven broken-symmetry states in doubly gated suspended bilayer graphene

              Amir Yacoby, Jens Martin, Benjamin Feldman … (2010)
              The non-interacting energy spectrum of graphene and its bilayer counterpart consists of multiple degeneracies owing to the inherent spin, valley and layer symmetries. Interactions among charge carriers are expected to spontaneously break these symmetries, leading to gapped ordered states. In the quantum Hall regime these states are predicted to be ferromagnetic in nature whereby the system becomes spin polarized, layer polarized or both. In bilayer graphene, due to its parabolic dispersion, interaction-induced symmetry breaking is already expected at zero magnetic field. In this work, the underlying order of the various broken-symmetry states is investigated in bilayer graphene that is suspended between top and bottom gate electrodes. By controllably breaking the spin and sublattice symmetries we are able to deduce the order parameter of the various quantum Hall ferromagnetic states. At small carrier densities, we identify for the first time three distinct broken symmetry states, one of which is consistent with either spontaneously broken time-reversal symmetry or spontaneously broken rotational symmetry.
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                Author and article information

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                Publication date Created: 11 September 2013
                Publication date Updated: 2013-11-18
                Article
                DOI: 10.1103/PhysRevB.88.205417
                ArXiV ID: 1309.2863
                SO-VID: 95d331b1-9c18-4ed5-bf03-91047192e16f
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
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                Journal reference Phys. Rev. B 88, 205417 (2013)
                Comments 15 pages, 8 figures, v2: to match published version
                Categories cond-mat.mes-hall

                ScienceOpen disciplines: Nanophysics
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                ScienceOpen disciplines: Nanophysics

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