Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene

We consider the effect of atomic impurities on the energy spectrum and electrical conductance of graphene. As is known, the ordering of atomic impurities at the nodes of a crystal lattice modifies the graphene spectrum of energy, yielding a gap in it. Assuming a Fermi level within the gap domain, th...

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Main Authors: Stefano Bellucci, Sergei Kruchinin, Stanislav P. Repetsky, Iryna G. Vyshyvana, Ruslan Melnyk
Format: Article
Language:English
Published: MDPI AG 2020-04-01
Series:Materials
Subjects:
Online Access:https://www.mdpi.com/1996-1944/13/7/1718
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spelling doaj-e1a77a0c38524dbd9f7e74fc80542f902020-11-25T02:43:22ZengMDPI AGMaterials1996-19442020-04-01131718171810.3390/ma13071718Behavior of the Energy Spectrum and Electric Conduction of Doped GrapheneStefano Bellucci0Sergei Kruchinin1Stanislav P. Repetsky2Iryna G. Vyshyvana3Ruslan Melnyk4INFN-Laboratori Nazionali di Frascati, 40 Via E. Fermi, 00044 Frascati, ItalyBogolyubov Institute for Theoretical Physics, NASU, Metrolohichna Str. 14-b, 03143 Kyiv, UkraineInstitute of High Technologies, Taras Shevchenko National University of Kiev, 4-g, Academician Glushkov Ave., 03022 Kiev, UkraineInstitute of High Technologies, Taras Shevchenko National University of Kiev, 4-g, Academician Glushkov Ave., 03022 Kiev, UkrainePhysical and Mathematical Sciences, National University “Kyevo-Mohylyans’ka Akademiya”, 2 G. Skovoroda Str., 04070 Kyiv, UkraineWe consider the effect of atomic impurities on the energy spectrum and electrical conductance of graphene. As is known, the ordering of atomic impurities at the nodes of a crystal lattice modifies the graphene spectrum of energy, yielding a gap in it. Assuming a Fermi level within the gap domain, the electrical conductance diverges at the ordering of graphene. Hence, we can conclude about the presence of a metal–dielectric transition. On the other hand, for a Fermi level occurring outside of the gap, we see an increase in the electrical conductance as a function of the order parameter. The analytic formulas obtained in the Lifshitz one-electron strong-coupling model, describing the one-electron states of graphene doped with substitutional impurity atoms in the limiting case of weak scattering, are compared to the results of numerical calculations. To determine the dependence of the energy spectrum and electrical conductance on the order parameter, we consider both the limiting case of weak scattering and the case of finite scattering potential. The contributions of the scattering of electrons on a vapor of atoms to the density of states and the electrical conductance of graphene with an admixture of interstitial atoms are studied within numerical methods. It is shown that an increase in the electrical conductance with the order parameter is a result of both the growth of the density of states at the Fermi level and the time of relaxation of electron states. We have demonstrated the presence of a domain of localized extrinsic states on the edges of the energy gap arising at the ordering of atoms of the admixture. If the Fermi level falls in the indicated spectral regions, the electrical conductance of graphene is significantly affected by the scattering of electrons on clusters of two or more atoms, and the approximation of coherent potential fails in this case.https://www.mdpi.com/1996-1944/13/7/1718grapheneenergy gapdensity of stateselectrical conductanceimpurity concentrationordering parameter
collection DOAJ
language English
format Article
sources DOAJ
author Stefano Bellucci
Sergei Kruchinin
Stanislav P. Repetsky
Iryna G. Vyshyvana
Ruslan Melnyk
spellingShingle Stefano Bellucci
Sergei Kruchinin
Stanislav P. Repetsky
Iryna G. Vyshyvana
Ruslan Melnyk
Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene
Materials
graphene
energy gap
density of states
electrical conductance
impurity concentration
ordering parameter
author_facet Stefano Bellucci
Sergei Kruchinin
Stanislav P. Repetsky
Iryna G. Vyshyvana
Ruslan Melnyk
author_sort Stefano Bellucci
title Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene
title_short Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene
title_full Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene
title_fullStr Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene
title_full_unstemmed Behavior of the Energy Spectrum and Electric Conduction of Doped Graphene
title_sort behavior of the energy spectrum and electric conduction of doped graphene
publisher MDPI AG
series Materials
issn 1996-1944
publishDate 2020-04-01
description We consider the effect of atomic impurities on the energy spectrum and electrical conductance of graphene. As is known, the ordering of atomic impurities at the nodes of a crystal lattice modifies the graphene spectrum of energy, yielding a gap in it. Assuming a Fermi level within the gap domain, the electrical conductance diverges at the ordering of graphene. Hence, we can conclude about the presence of a metal–dielectric transition. On the other hand, for a Fermi level occurring outside of the gap, we see an increase in the electrical conductance as a function of the order parameter. The analytic formulas obtained in the Lifshitz one-electron strong-coupling model, describing the one-electron states of graphene doped with substitutional impurity atoms in the limiting case of weak scattering, are compared to the results of numerical calculations. To determine the dependence of the energy spectrum and electrical conductance on the order parameter, we consider both the limiting case of weak scattering and the case of finite scattering potential. The contributions of the scattering of electrons on a vapor of atoms to the density of states and the electrical conductance of graphene with an admixture of interstitial atoms are studied within numerical methods. It is shown that an increase in the electrical conductance with the order parameter is a result of both the growth of the density of states at the Fermi level and the time of relaxation of electron states. We have demonstrated the presence of a domain of localized extrinsic states on the edges of the energy gap arising at the ordering of atoms of the admixture. If the Fermi level falls in the indicated spectral regions, the electrical conductance of graphene is significantly affected by the scattering of electrons on clusters of two or more atoms, and the approximation of coherent potential fails in this case.
topic graphene
energy gap
density of states
electrical conductance
impurity concentration
ordering parameter
url https://www.mdpi.com/1996-1944/13/7/1718
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