Concentration dependences of the elastic constants of the two-dimensional graphene-silicene system

The concentration dependences of the elastic constants of the two-dimensional Si _x C_{1 − x} system have been investigated with the use of the Harrison bonding-orbital method and the Keating model. The central and non-central force constants and the Grüneisen parameter have been considered by means of the bonding-orbital method. All quantities under consideration have been shown to exhibit a nonlinear behavior during the transition from graphene to silicene. A nontrivial role of the short-range repulsion has been discussed. The second-order and third-order elastic constants, the pressure dependences of the second-order elastic constants, as well as the Poisson’s ratio and Young’s modulus have been investigated in the Keating model. It has been found that the elastic constants and Young’s modulus change almost linearly upon the transition from graphene to silicene, whereas the other quantities under consideration exhibit nonlinearity.     

Elastic properties of graphene: The Keating model

The elastic properties of graphene have been described in terms of the Keating model. It has been shown that the two-dimensional structure of graphene is described by two independent elastic constants, like an isotropic solid. The Young’s modulus and the Poisson’s ratio have been determined. The results are compared with the experimental data obtained for graphite.     

Estimation of the Electron–Phonon Coupling Constants for Graphene and Metallic and Nonmetallic Substrates

Two modes of graphene–substrate interaction have been considered: a weak van der Waals bond and a strong covalent bond. The Lennard–Jones potential and Harrison bond-orbital method are used in the former and latter cases, respectively. Analytical expressions for the electron–phonon interaction constants, which contain only two parameters (binding energy E _B for graphene and a substrate and distance d between them) have been obtained. The constants have been calculated for metallic, semiconductor, and dielectric substrates.

     

Elastic characteristics of 2D carbon supracrystals as compared to graphene

The constants of the central and noncentral interactions between carbon atoms in 2D supracrystals, i.e., generalized two-dimensional crystals in which the sites of the lattice contain, instead of individual atoms, their symmetric complexes, have been calculated. It has been shown that these constants essentially depend on the symmetry of the 2D supracrystal and can significantly differ from the corresponding constants for graphene.     

Numerical simulation of graphene in a magnetic field within the effective field theory

Monte Carlo simulation of graphene in an external magnetic field perpendicular to the plane of graphene has been reported. The calculations have been performed using the effective quantum field theory with a noncompact (3 + 1)-dimensional Abelian gauge field and (2 + 1)-dimensional Kogut-Susskind fermions. It has been revealed that the external magnetic field shifts the semimetal-insulator phase transition point toward higher dielectric constants of the substrate. The phase diagram of the semimetal-insulator phase transition has been plotted in the (dielectric constant of the substrate-magnetic field) plane.     

Modifying a graphene layer by a thymine or a uracil nucleobase: DFT studies

The hybridizations of a graphene layer by a thymine and a uracil nucleobase have been investigated by performing density functional theory (DFT) calculations. The isolated and hybrid structures have been firstly stabilized to reach the minimum energy and the electronic properties have been subsequently evaluated for the optimized structures. The structural and atomic scale parameters indicated that the tip of graphene is important in determining the properties of new hybrids. Moreover, different effects of thymine and uracil nucleobases have been identified in the hybrid structures. Quadrupole coupling constants have been evaluated to characterize the atomic scale properties, in which the most notable effects of hybridizations have been observed for the atoms close to the linking regions whereas negligible effects have been seen for other atoms.     

Multiscale modeling of graphene- and nanotube-based reinforced polymer nanocomposites

A combination of molecular dynamics, molecular structural mechanics, and finite element method is employed to compute the elastic constants of a polymeric nanocomposite embedded with graphene sheets, and carbon nanotubes. The model is first applied to study the effect of inclusion of graphene sheets on the Young modulus of the composite. To explore the significance of the nanofiller geometry, the elastic constants of nanotube-based and graphene-based polymer composites are computed under identical conditions. The reinforcement role of these nanofillers is also investigated in transverse directions. Moreover, the dependence of the nanocomposite?s axial Young modulus on the presence of ripples on the surface of the embedded graphene sheets, due to thermal fluctuations, is examined via MD simulations. Finally, we have also studied the effect of sliding motion of graphene layers on the elastic constants of the nanocomposite.     

Quantum friction controlled by plasmons between graphene sheets

We theoretically study quantum friction between two infinite graphene sheets, which is controlled by plasmons excited at the interfaces of graphenes and dielectrics. In near-field regime, quantum friction can be enhanced due to the coupling of plasmons between two graphene sheets. Dependences of friction coefficient on distance, chemical potential of graphene, temperature of environment, and dielectric constant of substrate have been investigated in detail. Friction coefficient can be increased by increasing temperature or dielectric constants of substrates, and can be reduced by increasing distance or chemical potential.     

Dynamic properties of graphene

The phonon spectrum of graphene has been studied with the minimum set of the nearest neighbors in the Born-von Kármán model taking into account the electron-electron and electron-phonon interactions. The widths, both natural and owing to interactions with defects, of phonons have been estimated. Symmetry constraints imposed on force constants are taken into account. For symmetry reasons, vibrations with the polarization normal to the plane of the layer are not related to in-plane vibrations. The phonon frequencies at symmetry points and elastic moduli are expressed in terms of force constants.     

Third-order elastic moduli of single-layer graphene

In the framework of the Keating model with allowance made for the anharmonic constant of the central interaction between the nearest neighbors μ, analytical expressions have been obtained for three third-order independent elastic constants c _ijk (μ, ζ) of single-layer graphene, where ζ = (2α − β)/(4α + β) is the Kleinman internal displacement parameter and α and β are the harmonic constants of the central interaction between the nearest neighbors and the noncentral interaction between the next-nearest neighbors, respectively. The dependences of the second-order elastic constants on the pressure p have been determined. It has been shown that the moduli c ₁₁ and c ₂₂ differently respond to the pressure. Therefore, graphene is isotropic in the harmonic approximation, whereas the inclusion of anharmonicity leads to the appearance of the anisotropy.     

On the elastic characteristics of graphene and silicene

Analytical expressions for the central k ₀ and noncentral k ₁ force constants of two-dimensional (graphene, silicene) and three-dimensional (diamond, silicon) structures have been obtained within the previously proposed model of the binding energy of carbon atoms in graphene. The Kleinman internal displacement parameter of the two-dimensional structure has been determined. It has been shown that the ratio k ₀/k ₁ depends only on the dimension of the structure.     

Ellipsometry of anisotropic graphene-like two-dimensional materials on transparent substrates

New possibilities for determining anisotropic properties of the dielectric constants of two-dimensional materials by ellipsometry are developed. Graphene-like 2D materials are considered within the framework of macroscopic electrodynamics as ultrathin absorbing anisotropic films where the optical axis is perpendicular to the film surface. The ellipsometric inversion problem is resolved analytically. The resulting inversion formulas are very fast because they allow you to directly calculate the complex anisotropic dielectric constants without the use of sophisticated regression analysis or iterative root-finding procedures. In particular, the method offers an interest in graphene and related 2D materials because the anisotropic properties of such materials have not been studied to date.     

单层正三角锯齿型石墨烯量子点的电子结构和磁性

采用基于密度泛函理论的广义梯度近似(GGA),对不同尺寸(N=2—11)的单层正三角锯齿型石墨烯量子点(Z_N -GNDs)的结构进行优化,得到与实验数据较好符合的晶格常数,进一步计算得到不同尺寸下体系的自旋多重度、磁矩、电子态密度以及自旋电子密度.结果表明:所有体系都呈现金属性,在尺寸较小的体系中量子尺寸效应对电子结构的影响比较明显;与单层石墨烯片一样,sp²杂化作用和非键态电子在量子点中仍起到非常重要的作用;费米能级上有自旋向上的电子分布,体系的 关键词： 石墨烯 量子点 电子结构 磁性     

Phonons of graphene and graphitic materials derived from the empirical potential LCBOPII

We present the interatomic force constants and phonon dispersions of graphite and graphene from the LCBOPII empirical bond order potential. We find a good agreement with experimental results, particularly in comparison to other bond order potentials. From the flexural mode we determine the bending rigidity of graphene to be 0.69 eV at zero temperature. We discuss the large increase of this constant with temperature and argue that derivation of force constants from experimental values should take this feature into account. We examine also other graphitic systems, including multilayer graphene for which we show that the splitting of the flexural mode can provide a tool for characterization.     

Electromagnetic waves reflection,transmission and absorption by graphene–magnetic semiconductor–graphene sandwich-structure in magnetic field: Faraday geometry

Electrodynamic properties of the graphene–magnetic semiconductor–graphene sandwich-structure have been investigated theoretically with taking into account the dissipation processes. Influence of graphene layers on electromagnetic waves propagation in graphene–semi-infinte magnetic semiconductor and graphene–magnetic semiconductor–graphene sandwich-structure has been analyzed. Frequency and field dependences of the reflectance, transmittance and absorbtance of electromagnetic waves by such structure have been calculated. The size effects associated with the thickness of the structure have been analyzed. The possibility of efficient control of electrodynamic properties of graphene–magnetic semiconductor–graphene sandwich-structure by an external magnetic field has been shown.     

To the theory of adsorption on epitaxial graphene: Model approach

A model of adsorption on epitaxial graphene has been constructed in two stages: first, the density of states of a graphene monolayer adsorbed on a solid substrate has been found and then an adsorbed atom has been placed on the epitaxial graphene thus formed. Metallic and semiconductor substrates have been considered. Charge transfer between the adatom and epitaxial graphene has been calculated. The roles of the substrate and graphene layer in the formation of the electronic state of adatoms have been estimated.     

On the Dispersion Relation of Plasmons in a Gapless-Graphene-Based Superlattice with Alternating Fermi Velocity

A graphene-based superlattice formed owing to the periodic modulation of the Fermi velocity is considered. Such a modulation is possible in graphene deposited on a strip substrate of materials with significantly different static dielectric constants. The dispersion relation for plasmons has been derived for this system in the case where the Fermi level lies in the low miniband. The problem of absorption of modulated external electromagnetic radiation because of the excitation of plasmons has been discussed.     

Transport properties of epitaxial graphene formed on the surface of a metal

The transport properties of epitaxial graphene formed on the surface of a metal substrate have been considered within the approach based on the model Anderson-Newns Hamiltonian. An analytical expression for the density of states of epitaxial graphene has been obtained and the renormalization of the Fermi velocity in doped epitaxial graphene has been investigated. The real part of the dynamic conductance of epitaxial graphene has been examined and the limiting values of conductance have been analyzed. When there is no interaction between the graphene and the substrate, the static conductance of epitaxial graphene takes on the universal value 2e ²/π² ?. The fundamental problems considered in this study are of crucial importance in the study of optical, magneto-optical, thermoelectric, and thermomagnetic properties of epitaxial graphene. The obtained results are of great interest for practical use of epitaxial graphene as a promising material for microwave technology.     

Theoretical calculation of excitonic binding energies and optical absorption spectra for Armchair graphene nanoribbons

In this paper the excitons of armchair graphene nanoribbons with layers of different width and thickness have been investigated. In this investigation, the band structure and energy gap of armchair graphene nanoribbons have been calculated using a tight-binding model including edge deformation effects (all edge atoms have been passivated with hydrogen atoms). Also, by calculating the conductance in armchair graphene nanoribbons (A-GNRs) optical absorption of armchair graphene nanoribbon in the single-electron approximation has been obtained. Finally, the binding energy of excitons in armchair graphene nanoribbons has been calculated using the Wannier model, Hartree-Fock approximation and the Bethe-Salpeter equation.     

Microwave-assisted covalent modification of graphene nanosheets with chitosan and its electrorheological characteristics

Biofunctionalization and manipulating of graphene nanosheets (GNS) are important for biomedical research and application. Chitosan (CS) modified graphene nanosheets have been successfully prepared under microwave irradiation in N,N-dimethylformamide medium, which involved the reaction between the carboxyl groups of graphene oxide nanosheets (GONS) and the amido groups of chitosan followed by the reduction of graphene oxide nanosheets into graphene nanosheets using hydrazine hydrate. The as-prepared graphene nanosheets-chitosan (GNS-CS) nanocomposites have been characterized by FTIR, TEM, FESEM, XRD and TG. The results showed that chitosan was covalently grafted onto the surface of graphene nanosheets via amido bonds. Solubility measurements indicated that the resultant nanocomposites dispersed well in aqueous acetic acid. Especially, the electrorheological (ER) properties of the GNS-CS nanocomposites have been investigated. It is believed that this new nanocomposites may be promising for biomedical applications.