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      Quantum electrodynamics with anisotropic scaling: Heisenberg-Euler action and Schwinger pair production in the bilayer graphene

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          Abstract

          We discuss quantum electrodynamics emerging in the vacua with anisotropic scaling. Systems with anisotropic scaling were suggested by Horava in relation to the quantum theory of gravity. In such vacua the space and time are not equivalent, and moreover they obey different scaling laws, called the anisotropic scaling. Such anisotropic scaling takes place for fermions in bilayer graphene, where if one neglects the trigonal warping effects the massless Dirac fermions have quadratic dispersion. This results in the anisotropic quantum electrodynamics, in which electric and magnetic fields obey different scaling laws. Here we discuss the Heisenberg-Euler action and Schwinger pair production in such anisotropic QED

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          The electronic properties of graphene

          K. S. Novoselov, A. K. Geim, A. H. Castro Neto … (2007)
          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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            Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator

            Ashvin Vishwanath, Ari M. Turner, Xiangang Wan … (2010)
            In 5d transition metal oxides such as the iridates, novel properties arise from the interplay of electron correlations and spin-orbit interactions. We investigate the electronic structure of the pyrochlore iridates, (such as Y\(_{2}\)Ir\(_{2}\)O\(_{7}\)) using density functional theory, LDA+U method, and effective low energy models. A remarkably rich phase diagram emerges on tuning the correlation strength U. The Ir magnetic moment are always found to be non-collinearly ordered. However, the ground state changes from a magnetic metal at weak U, to a Mott insulator at large U. Most interestingly, the intermediate U regime is found to be a Dirac semi-metal, with vanishing density of states at the Fermi energy. It also exhibits topological properties - manifested by special surface states in the form of Fermi arcs, that connect the bulk Dirac points. This Dirac phase, a three dimensional analog of graphene, is proposed as the ground state of Y\(_{2}\)Ir\(_{2}\)O\(_{7}\) and related compounds. A narrow window of magnetic `axion' insulator, with axion parameter \(\theta=\pi\), may also be present at intermediate U. An applied magnetic field induces ferromagnetic order and a metallic ground state.
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              Weyl Semimetal in a Topological Insulator Multilayer

              Leon Balents, A A Burkov (2011)
              We propose a simple realization of the three-dimensional (3D) Weyl semimetal phase, utilizing a multilayer structure, composed of identical thin films of a magnetically-doped 3D topological insulator (TI), separated by ordinary-insulator spacer layers. We show that the phase diagram of this system contains a Weyl semimetal phase of the simplest possible kind, with only two Dirac nodes of opposite chirality, separated in momentum space, in its bandstructure. This particular type of Weyl semimetal has a finite anomalous Hall conductivity, chiral edge states, and occurs as an intermediate phase between an ordinary insulator and a 3D quantum anomalous Hall insulator with a quantized Hall conductivity, equal to \(e^2/h\) per TI layer. We find that the Weyl semimetal has a nonzero DC conductivity at zero temperature and is thus an unusual metallic phase, characterized by a finite anomalous Hall conductivity and topologically-protected edge states.
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                Author and article information

                Journal
                Publication date Created: 07 March 2012
                Publication date Updated: 2012-03-19
                Article
                DOI: 10.1134/S0021364012080061
                ArXiV ID: 1203.1578
                SO-VID: 95dac889-71f4-48dd-823e-ef0b72271857
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                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Journal reference Pis'ma ZhETF 95, 457-461 (2012)
                Comments 5 pages, no figures, JETP Letters style, version accepted in JETP Letters
                Categories cond-mat.str-el cond-mat.mes-hall gr-qc hep-ph

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