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      Flat Bands near Fermi Level of Topological Line Defects on Graphite

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          Abstract

          Flat bands play an important role in the study of strongly correlated phenomena, such as ferromagnetism, superconductivity, and fractional quantum Hall effect. Here we report direct experimental evidence for the presence of flat bands, close to the Fermi level, in one-dimensional topological defects on graphite seen as a pronounced peak in the tunnelling density of states. Our ab initio calculations indicate that the flat bands with vanishing Fermi velocity originate from sp2 dangling bonds (with antibonding nature) of undercoordinated carbon atoms at the edges of the defects. We further demonstrate that the presence of flat bands could be a universal behavior of 1D defects of graphene/graphite with undercoordinated carbon atoms at the edges of the defects.

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          Two-Dimensional Gas of Massless Dirac Fermions in Graphene

          Electronic properties of materials are commonly described by quasiparticles that behave as non-relativistic electrons with a finite mass and obey the Schroedinger equation. Here we report a condensed matter system where electron transport is essentially governed by the Dirac equation and charge carriers mimic relativistic particles with zero mass and an effective "speed of light" c* ~10^6m/s. Our studies of graphene - a single atomic layer of carbon - have revealed a variety of unusual phenomena characteristic of two-dimensional (2D) Dirac fermions. In particular, we have observed that a) the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; b) graphene's conductivity never falls below a minimum value corresponding to the conductance quantum e^2/h, even when carrier concentrations tend to zero; c) the cyclotron mass m of massless carriers with energy E in graphene is described by equation E =mc*^2; and d) Shubnikov-de Haas oscillations in graphene exhibit a phase shift of pi due to Berry's phase.
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            The electronic properties of graphene

            This article reviews the basic theoretical aspects of graphene, a one atom thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. We show that the Dirac electrons behave in unusual ways in tunneling, confinement, and integer quantum Hall effect. We discuss the electronic properties of graphene stacks and show that they vary with stacking order and number of layers. Edge (surface) states in graphene are strongly dependent on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. We also discuss how different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.
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              Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene

              When electrons are confined in two-dimensional (2D) materials, quantum mechanically enhanced transport phenomena, as exemplified by the quantum Hall effects (QHE), can be observed. Graphene, an isolated single atomic layer of graphite, is an ideal realization of such a 2D system. Here, we report an experimental investigation of magneto transport in a high mobility single layer of graphene. Adjusting the chemical potential using the electric field effect, we observe an unusual half integer QHE for both electron and hole carriers in graphene. Vanishing effective carrier masses is observed at Dirac point in the temperature dependent Shubnikov de Haas oscillations, which probe the 'relativistic' Dirac particle-like dispersion. The relevance of Berry's phase to these experiments is confirmed by the phase shift of magneto-oscillations, related to the exceptional topology of the graphene band structure.
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                Author and article information

                Journal
                05 July 2012
                Article
                10.1063/1.4752441
                1207.1494
                aa0c612a-dfea-4444-a109-8ef45f70a614

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Appl. Phys. Lett. 101, 113113, (2012)
                cond-mat.mes-hall

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