Graphene layer number dependent size distribution of silver nanoparticles

We observe that silver atoms deposited by thermal evaporation deposition onto n-layer graphene films condense upon annealing to form nanoparticles with an average diameter and density that is determined by the layer numbers of graphene films. The optical microscopy and Raman spectroscopy were utilized to identify the number of the graphene layers and the SEM (scanning electron microscopy) was used to observe the morphologies of the particles. Systematic analysis revealed that the average sizes of the nanoparticles increased with the number of graphene layers. The density of nanoparticles decreased as the number of graphene layers increased, revealing a large variation in the surface diffusion strength of nanoparticles on the different substrates. The mechanisms of formation of these layer-dependent morphologies of silver nanoparticles are related to the surface free energy and surface diffusion of the n-layer graphenes.     

Multilayer graphene waveguides

We study dispersion properties of TM-polarized electromagnetic waves guided by a multilayer graphene metamaterial. We demonstrate that both dispersion and localization of the guided modes can be efficiently controlled by changing the number of layers in the structure. Remarkably, we find that in the long wavelength limit, the dispersion of the fundamental mode of the N-layer graphene structure coincides with the dispersion of a plasmon mode supported by a single graphene layer, but with N times larger conductivity. We also compare our exact dispersion relations with the results provided by the effective media model.     

光抽运多层石墨烯太赫兹表面等离子体增益特性的研究

本文建立了光抽运多层石墨烯表面等离子体模型,计算了光抽运多层石墨烯等离子体传播系数的实部和吸收系数,讨论了动量弛豫时间、温度、层数、准费米能级对表面等离子体传播系数的实部和吸收系数的影响.研究结果表明,光抽运多层石墨烯使其动态电导率的实部在太赫兹频段内出现负值时,石墨烯表面等离子体实现增益.通过光抽运剥离层石墨烯和含有底层石墨烯结构表面等离子体传播系数和吸收系数比较,表明光抽运剥离层石墨烯能更有效地实现表面等离子体的增益.同时,在低温下,光抽运具有合适层数的石墨烯比光抽运单层石墨烯能获得更大的表面等离子体增益.     

Coherent nonlinear electromagnetic response in twisted bilayer and few-layer graphene

The phenomenon of Rabi oscillations far from resonance is described in bilayer and few-layer graphene. These oscillations in the population and polarization at the Dirac point in n-layer graphene are seen in the nth harmonic term in the external driving frequency. The underlying reason behind these oscillations is attributable to the pseudospin degree of freedom possessed by all these systems. Conventional Rabi oscillations, which occur only near resonance, are seen in multiple harmonics in multilayer graphene. However, the experimentally measurable current density exhibits anomalous behaviour only in the first harmonic in all the graphene systems. A fully numerical solution of the optical Bloch equations is in complete agreement with the analytical results, thereby justifying the approximation schemes used in the latter. The same phenomena are also described in twisted bilayer graphene with and without an electric potential difference between the layers. It is found that the anomalous Rabi frequency is strongly dependent on twist angle for weak applied fields – a feature absent in single-layer graphene, whereas the conventional Rabi frequency is relatively independent of the twist angle.     

Modelling self-assembling of colloid particles in multilayered structures

Simulations of particle multilayer build-up in the layer by layer (LbL) self-assembling processes have been performed according to the generalized random sequential adsorption (RSA) scheme. The first (precursor) layer having an arbitrary coverage of adsorption centers was generated using the standard RSA scheme pertinent to homogeneous surface. Formation of the consecutive layers (up to 20) was simulated by assuming short-range interaction potentials for two kinds of particles of equal size. Interaction of two particles of different kind resulted in irreversible and localized adsorption upon their contact, whereas particles of the same kind were assumed to interact via the hard potential (no adsorption possible). Using this algorithm theoretical simulations were performed aimed at determining the particle volume fraction as a function of the distance from the interface, as well as the multilayer film roughness and thickness as a function of the number of layers. The simulations revealed that particle concentration distribution in the film was more uniform for low precursor layer density than for higher density, where well-defined layers of closely packed particles appeared. On the other hand, the roughness of the film was the lowest at the highest precursor layer density. It was also predicted theoretically that for low precursor layer density the film thickness increased with the number of layers in a non-linear way. However, for high precursor layer density, the film thickness increased linearly with the number of layers and the average layer thickness was equal to 1.58 of the particle radius, which is close to the closely packed hexagonal layer thickness equal to 1.73. It was concluded by analysing the existing data for colloid particles and polyelectrolytes that the theoretical results can be effectively exploited for interpretation of the LbL processes involving colloid particles and molecular species like polymers or proteins.     

Charge-transfer-induced cesium superlattices on graphene

We investigate cesium (Cs) adsorption on graphene formed on a 6H-SiC(0001) substrate by a combined scanning tunneling microscopy and density functional theory study. Individual Cs atoms adsorb preferentially at the rim region of the well-defined 6×6 substrate superstructure and on multilayer graphene. By finely controlling the graphene thickness and Cs coverages (1/3 ML and 1?ML), we here demonstrate two intriguing and well-ordered Cs superlattices on bilayer and multilayer graphene (<6 layers). Statistical analysis of the Cs-Cs interatomic distance reveals a hitherto unobserved Cs-Cs long-range electrostatic potential caused by charge transfer from Cs to graphene, which couples with the inhomogeneous substrate potential to stabilize the observed Cs superlattices. The present study provides a new avenue to fabricate atomic and molecular superlattices for applications in high-density recording and data storage.     

Band topology and the quantum spin Hall effect in bilayer graphene

We consider bilayer graphene in the presence of spin-orbit coupling, in order to assess its behavior as a topological insulator. The first Chern number n for the energy bands of single-layer graphene and that for the energy bands of bilayer graphene are computed and compared. It is shown that for a given valley and spin, n for a Bernal-stacked bilayer is doubled with respect to that for the monolayer. This implies that this form of bilayer graphene will have twice as many edge states as single-layer graphene, which we confirm with numerical calculations and analytically in the case of an armchair terminated surface. Bernal-stacked bilayer graphene is a weak topological insulator, whose surface spectrum is susceptible to gap opening under spin-mixing perturbations. We assess the stability of the associated topological bulk state of bilayer graphene under various perturbations. In contrast, we show that AA-stacked bilayer graphene is not a topological insulator unless the spin-orbit coupling is bigger than the interlayer hopping. Finally, we consider an intermediate situation in which only one of the two layers has spin-orbit coupling, and find that although individual valleys have non-trivial Chern numbers for the case of Bernal stacking, the spectrum as a whole is not gapped, so the system is not a topological insulator.     

Coulomb bare interactions in inhomogeneous 4-layer graphene structures

We investigate Coulomb bare interactions in 4-layer graphene systems, taking into account the inhomogeneity of dielectric environment. By solving Poisson equation in momentum space, 16 elements of Coulomb potential tensor have been formed with analytical expressions. The formulae illustrate that Coulomb bare interactions in inhomogeneous 4-layer graphene system differ noticeably from those in homogeneous one. Nevertheless, both intra- and interlayer Coulomb potentials become independent with dielectric constants of contacting media, but they are decided by those of dielectric layer surrounding the system in long wavelength approximation. Besides, numerical results demonstrate that Coulomb bare interactions decrease considerably with the increase in carrier density in graphene sheets as well as their separated distance. In all investigations, the inhomogeneity of dielectric background should not be neglected for improvement in the model.     

Epitaxial growth of a graphene single crystal on the Ni(111) surface

The thermally controlled synthesis of graphene from propylene molecules on the Ni(111) surface in ultrahigh vacuum is studied by scanning tunneling microscopy and density functional theory. It is established that the adsorption of propylene on Ni(111) atomic terraces at room temperature results in the dehydration of propylene molecules with the formation of single-atomic carbon chains and in the complete dissociation of propylene at the edges of atomic steps with the subsequent diffusion of carbon atoms below the surface. The annealing of such a sample at 500°С leads to the formation of multilayer graphene islands both from surface atomic chains and by the segregation of carbon atoms collected in the upper nickel atomic layers. The process of formation of an epitaxial graphene monolayer until the complete filling of the nickel surface is controllably observed. Atomic defects seen on the graphene surface are interpreted as individual nickel atoms incorporated into graphene mono- or bivacancies.     

Domain growth and aging scaling in coarsening disordered systems

We explore the electronic and transport properties out of a biased multilayer hexagonal boron nitride (h-BN) by first-principles calculations. The band gaps of multilayer h-BN decrease almost linearly with increasing perpendicular electric field, irrespective of the layer number N and stacking manner. The critical electric filed (E ₀) required to close the band gap decreases with the increasing N and can be approximated by E ₀ = 3.2 / (N ? 1) (eV). We provide a quantum transport simulation of a dual-gated 4-layer h-BN with graphene electrodes. The transmission gap in this device can be effectively reduced by double gates, and a high on-off ratio of 3000 is obtained with relatively low voltage. This renders biased MLh-BN a promising channel in field effect transistor fabrication.     

Theoretical investigation of structures and energetics of sodium adatom and its dimer on graphene: DFT study

Extensive ab initio calculations have been performed to study the energetics of a sodium (Na) atom and its dimer adsorbed on graphene using the SIESTA package Soler et al. (2002) [1] which works within a DFT(density functional theory)–GGA (generalized gradient approximation) pseudopotential framework. The adsorption energy, geometry, charge transfer, ionization potential and density of states (DOS), partial density states (PDOS) of adatom/dimer-graphene system have been calculated. After considering various sites for adsorption of Na on graphene, the center of a hexagonal ring of carbon atoms is found to be the preferred site of adsorption while the Na₂ dimer prefers to rest parallel to the graphene sheet. We find insignificant energy differences among adsorption configurations involving different possible sites in parallel orientation, which implies high mobility of the dimer on the graphene sheet. We also notice only a slight distortion of the graphene sheet perpendicular to its plane upon adatom adsorption. However, some lateral displacements seen are more perceptible.     

Surface potentials of few-layer graphene films in high vacuum and ambient conditions

The surface potentials of few-layer graphene (FLG) films in high vacuum and ambient conditions have been investigated by employing electrostatic force microscopy. It is found that the surface potential of FLG films in ambient air has a constant large depression compared to that measured in a high vacuum. Our experimental results indicate that the shift is most likely caused by the presence of ambient adsorbates on the outmost graphene surfaces. The surface potentials increase with the number of graphene layers and approach the bulk value for five or more graphene layers in high vacuum as well as in ambient air. Since the contribution of the surface adsorbates is a constant value, we further show that the thickness dependence of the surface potential can be sufficiently explained by the nonlinear Thomas-Fermi Theory in both conditions.     

Density functional study of TaSin (n = 1-3, 12) clusters adsorbed to graphene surface

A plane-wave density functional theory (DFT) calculations have been performed to investigate structural and electronic properties of TaSi_n (n = 1-3, 12) clusters supported by graphene surface. The resulting adsorption structures are described and discussed in terms of stability, bonding, and electron transfer between the cluster and the graphene. The TaSi_n clusters on graphene surface favor their free-standing ground-state structures. Especially in the cases of the linear TaSi₂ and the planar TaSi₃, the graphene surface may catalyze the transition of the TaSi_n clusters from an isomer of lower dimensionality into the ground-state structure. The adsorption site and configuration of TaSi_n on graphene surface are dominated by the interaction between Ta atom and graphene. Ta atom prefers to adsorb on the hollow site of graphene, and Si atoms tend to locate on the bridge site. Further, the electron transfer is found to proceed from the cluster to the surface for n = 1 and 2, while its direction reverses as n > 2. For the case of TaSi, chemisorption is shown to prevail over physisorption as the dominant mode of surface-adsorbate interaction by charge density analysis.     

Topological insulators in ternary compounds with a honeycomb lattice

We investigate a new class of ternary materials such as LiAuSe and KHgSb with a honeycomb structure in Au-Se and Hg-Sb layers. We demonstrate the band inversion in these materials similar to HgTe, which is a strong precondition for existence of the topological surface states. In contrast with graphene, these materials exhibit strong spin-orbit coupling and a small direct band gap at the Γ point. Since these materials are centrosymmetric, it is straightforward to determine the parity of their wave functions, and hence their topological character. Surprisingly, the compound with strong spin-orbit coupling (KHgSb) is trivial, whereas LiAuSe is found to be a topological insulator.     

铜表面抗氧化性能与其覆盖石墨烯的层数依赖关系研究

We studied the oxidation resistance of graphene-coated Cu surface and its layer dependence by directly growing monolayer graphene with different multilayer structures coexisted, di-minishing the influence induced by residue and transfer technology. It is found that the Cu surface coated with the monolayer graphene demonstrate tremendous difference in oxidation pattern and oxidation rate, compared to that coated with the bilayer graphene, which is considered to be originated from the strain-induced linear oxidation channel in monolayer graphene and the intersection of easily-oxidized directions in each layer of bilayer graphene, respectively. We reveal that the defects on the graphene basal plane but not the boundaries are the main oxidation channel for Cu surface under graphene protection. Our finding indi-cates that compared to putting forth efforts to improve the quality of monolayer graphene by reducing defects, depositing multilayer graphene directly on metal is a simple and effective way to enhance the oxidation resistance of graphene-coated metals.     

Adsorption compression in surface layers

A recently elucidated aspect of adsorption, compression in confined phases, is discussed. Grand Canonical Monte Carlo simulations were performed for the adsorption of Lennard–Jones molecules and new details of intermolecular interactions in adsorbed layers are analysed. It is shown that a strong attraction to a surface can cause adsorption compression not only in the first layer, but also in higher layers. Compression of the first layer creates a pattern of active sites; the second layer tends to be commensurate with this pattern and has density higher than that of a ‘free’ layer. This pattern propagates to higher layers. However, there is a wide range of chemical potentials where the first layer is compressed and the second layer is not yet formed. It was found that transition to adsorption compression results in oscillations of the isosteric heat of adsorption. These oscillations are determined by a combination of (a) changes in adsorbed layers’ structure and (b) exchange of molecules between layers. In particular, at high affinity to adsorbent, the adsorption isotherm for the first layer has a slight maximum because an increase of the chemical potential causes molecules to leave the compressed first layer and move to the second layer. For this reason, the isosteric heat of adsorption decreases and can become negative. Analysis of adsorption compression mechanisms in the context of theory and emerging experimental results indicates that the significance of this phenomenon is not limited to fundamental aspects of adsorption and capillarity. These mechanisms play a crucial role in various applications, such as heterogeneous catalysis, membrane separations, and self-assembly on surfaces. Results are discussed in a broader context of theory, experiments and previous simulations.     

三层石墨烯及其n型和p型插层化合物的制备和拉曼光谱表征

我们利用微机械剥离方法制备了三层石墨烯.在此基础上,利用两室气体传输法,以三氯化铁和钾为化学掺杂剂,成功合成了三层石墨烯的一阶p型和n型插层化合物.三层石墨烯的高分辨率拉曼光谱具有独特的2D谱峰线形,该线形可以用作指纹来鉴别三层石墨烯.三层石墨烯一阶插层化合物的拉曼光谱表明,三氯化铁和钾的插层掺杂使得三层石墨烯的层间耦...     

A continuum model of a multilayer nanosheet

A continuum model for describing the bending and free vibrations of a crystalline graphite sheet consisting of graphene layers is proposed. Graphene is modeled by a two-dimensional layer having a finite rigidity under extension and bending. The interval between graphene layers through which their Van-der-Waals interaction occurs is modeled by a fictitious layer with relatively low rigidity. In the solution, formulas describing the bending of a multilayer sheet with alternating rigid and soft layers are used.     

Sodium Intercalation of Graphene Films on Re( $$10\bar 10$$ 10 1 ¯ 0 )

It is shown that during low-temperature (300–500 K) intercalation of sodium atoms into thin multilayer graphene and graphite films on rhenium the first graphene layer plays the role of a trap to which atoms coming on the surface diffuse through a graphite film. The intercalation phase of the interlayer space in the graphite bulk is actively filled at a sodium atoms concentration under the first graphene layer close to the maximum possible (2 ± 0.5) × 10¹⁴ cm^–2. This phase capacity is proportional to the graphite film thickness that can be varied in this work from one graphene layer to ~50 atomic layers. The diffusion energy E _d of Na atoms through the graphite film was estimated to be E _d ≈ 1.4 eV.

     

The computations of reflection coefficients of multilayer structure based on the reformulation of Thomson-Haskell method

A reformulation of the Thomson-Haskell method is presented for calculating the reflection coefficients of multilayer structure immersing in the coupling fluid. Instead of directly multiplying the layer propagator matrix, the new method splits the layer propagator matrix and excursively determines the interface stiffness matrix starting from the bottom half-space with known stiffness. A formulation for the reflection coefficients is derived based on the obtained interface stiffness matrix of the top layer. This scheme can be applied to a single solid layers or layered structures containing both fluid and solid layers. It keeps the simplicity but naturally excludes the exponential growth term and thus can be applied at any frequency range. Its validity and feasibility were experimentally proved by the measurement of the reflection coefficients of a three layered structure of aluminum–glass–aluminum and a sandwiched layer structure of two 250 μm stainless plates filled with 100 μm deionized water based on the inversion of V(z, t) technique. The result of experiments is consistent with the theoretical calculation. The reformulation of the Thomson-Haskell method offers an efficient and effective solution for calculating the acoustic reflection coefficients of multilayer structures of any configurations.