Dependence of the Electronic Structure of a Graphene Nanoribbon on the Concentration of Adsorbed Particles
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ence of the Electronic Structure of a Graphene Nanoribbon on the Concentration of Adsorbed Particles S. Yu. Davydov Ioffe Physical Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia e-mail: [email protected] Received March 18, 2020; revised March 26, 2020; accepted March 26, 2020
Abstract—The effect of the indirect exchange of particles adsorbed on a graphene nanoribbon on the width of the induced energy gap and the effective mass of carriers is studied. Analytical dependences of these characteristics on the concentration of adparticles, the adsorbate–substrate binding energy, and the energy level of the adsorbed particle are obtained. Keywords: graphene nanoribbon with zigzag edges, indirect interaction of adparticles, energy gap, effective mass. DOI: 10.1134/S1063785020070068
The unique properties of graphene that allow one to use it under extreme conditions make this material very promising for nanoelectronics [1–3]. The absence of an energy gap in the spectrum of an ideal (pure, defect-free, and mechanically unstressed) infinite free (i.e., in the absence of a substrate) graphene sheet is a particular obstacle in this way. To create a gap, it is necessary to violate the conditions of ideality [4, 5]. The adsorption of foreign atoms is one of the methods used for this purpose [6–8]. The overwhelming majority of theoretical studies devoted to the adsorption on graphene were performed within the framework of the density functional theory (DFT) method [6–10]. Here, we investigate the particles interacting with each other at various concentrations by using the method of Green functions [11, 12]. It is known [12, 13] that there are three main channels of interaction between adatoms. The first channel is electrostatic repulsion of parallel dipoles formed by adatoms and their images in the substrate under the condition of charge transition. The second channel is direct exchange, i.e., direct transition of electrons between adatoms at a high concentration thereof when the orbitals of the nearest neighbors overlap. Finally, the third channel is indirect exchange of electrons between adatoms through the band states of the substrate. Indirect exchange, being long-range like the dipole interaction, manifests itself even with small surface coverages. Previously [14], we have studied the inf luence of the dipole–dipole repulsion and indirect exchange on the charge of adatoms. The role of
direct exchange is easily understood from the consideration of small atomic clusters on the surface of graphene [14, 15]. As was shown in [14, 15], the dipole–dipole repulsion and direct exchange do not lead to the appearance of an energy gap. In the electronic spectrum of a graphene sheet, the indirect exchange induces energy gap ΔL = ε2a + 4ΘV 2 [16], where εa is the energy level of an adsorbed particle, which is measured from the Dirac point; V is the adsorbate–substrate matrix element averaged over the Brillouin zone of graphene; and Θ = Na/NML is the degree of surface coverage by the adsaorbate (Na ≠ 0
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