Graphene electronic structure in charge density waves
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Oscar J. Hernandez Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada; and TRIUMF, Vancouver, British Columbia V6T 2A3, Canada
Mingsu Si Key Laboratory for Magnetism and Magnetic Materials, Lanzhou University, Lanzhou 730000, People’s Republic of China
Zhoufei Wang Department of Physics, College of Science, South China Agricultural University, Guangzhou 510642, People’s Republic of China (Received 9 May 2017; accepted 16 June 2017)
We introduce the idea that the electronic band structure of a charge density wave system may mimic that of graphene. In that case, a class of materials quite different from graphene might be opened up to exploit graphene’s remarkable properties. For such materials, their dynamical rather than static properties are crucial. The charge density wave system requires a wave geometry simply related to graphene and self-consistency among the electrons which requires the net Coulomb and phonon-mediated parts of the electron–electron interactions to be attractive. Our model leads to an analytical expression for the total energy in terms of the effective electron mass l, the electron density q0, and the strength ~vK of the net electron–electron interaction. We examine the limitations set upon ~vK by self-consistency, stability, and the approximation in the electronic state calculation and find them to be mutually compatible.
I. INTRODUCTION
A simplified model of graphene consists of a planar hexagonal array of carbon atoms (C). Its electronic band structure was first determined by Wallace in a 1947 study of graphite.1 It was first isolated and studied in detail by Novoselov et al. in 2004.2 Since then, it has been intensively studied, particularly for its potential value as a technological material. It has been found to have a number of extraordinary properties, including high electronic conductivity and enormous strength. The ground state electronic structure of graphene consists of a filled hexagonal first Brillouin zone (BZI), with an energy gap that goes monotonically to zero at the zone corners, from a maximum at the centers of the zone edges. This electronic configuration arises from the particular relationship between the number of conduction (noncore) electrons per atom and the hexagonal atomic ordering. A simple model of the noncore electrons in graphene has a two-dimensional Hamiltonian consisting of electron kinetic energy, electron–core (EC) interactions, and electron–electron (EE) interactions. Two extreme Contributing Editor: Susan B. Sinnott a) Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/jmr.2017.265
approximations from this formulation consist of the limiting cases: (i) where EE interactions are negligible compared to EC interactions and (ii) where EC are negligible compared to EE. Wallace’s treatment for the band structure falls within case (i). Case (ii) is representative of models for superconductivity (SC) and for charge density waves (CDWs). The theoretical basis for the lat
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