A Tight-Binding Grand Canonical Monte Carlo Study of the Catalytic Growth of Carbon Nanotubes

The nucleation of carbon nanotubes on small nickel clusters is studied using a tight binding model coupled to grand canonical Monte Carlo simulations. This technique closely follows the conditions of the synthesis of carbon nanotubes by chemical vapor deposition. The possible formation of a carbon cap on the catalyst particle is studied as a function of the carbon chemical potential, for particles of different size, either crystalline or disordered. We show that these parameters strongly influence the structure of the cap/particle interface which in turn will have a strong effect on the control of the structure of the nanotube. In particular, we discuss the presence of carbon on surface or in subsurface layers

Nickel assisted healing of defective graphene

The healing of graphene grown from a metallic substrate is investigated using tight-binding Monte Carlo simulations. At temperatures (ranging from 1000 to 2500 K), an isolated graphene sheet can anneal a large number of defects suggesting that their healing are thermally activated. We show that in presence of a nickel substrate we obtain a perfect graphene layer. The nickel-carbon chemical bonds keep breaking and reforming around defected carbon zones, providing a direct interaction, necessary for the healing. Thus, the action of Ni atoms is found to play a key role in the reconstruction of the graphene sheet by annealing defects

Long-range interactions between substitutional nitrogen dopants in graphene: electronic properties calculations

Being a true two-dimensional crystal, graphene has special properties. In particular, a point-like defect in graphene may have effects in the long range. This peculiarity questions the validity of using a supercell geometry in an attempt to explore the properties of an isolated defect. Still, this approach is often used in ab-initio electronic structure calculations, for instance. How does this approach converge with the size of the supercell is generally not tackled for the obvious reason of keeping the computational load to an affordable level. The present paper addresses the problem of substitutional nitrogen doping of graphene. DFT calculations have been performed for 9x9 and 10x10 supercells. Although these calculations correspond to N concentrations that differ by about 10%, the local densities of states on and around the defects are found to depend significantly on the supercell size. Fitting the DFT results by a tight-binding Hamiltonian makes it possible to explore the effects of a random distribution of the substitutional N atoms, in the case of finite concentrations, and to approach the case of an isolated impurity when the concentration vanishes. The tight-binding Hamiltonian is used to calculate the STM image of graphene around an isolated N atom. STM images are also calculated for graphene doped with 0.5 % concentration of nitrogen. The results are discussed in the light of recent experimental data and the conclusions of the calculations are extended to other point defects in graphene

Exciton interference in hexagonal boron nitride

In this letter we report a thorough analysis of the exciton dispersion in bulk hexagonal boron nitride. We solve the ab initio GW Bethe-Salpeter equation at finite $\mathbf{q}\parallel \Gamma K$, and we compare our results with recent high-accuracy electron energy loss data. Simulations reproduce the measured dispersion and the variation of the peak intensity. We focus on the evolution of the intensity, and we demonstrate that the excitonic peak is formed by the superposition of two groups of transitions that we call $KM$ and $MK'$ from the k-points involved in the transitions. These two groups contribute to the peak intensity with opposite signs, each damping the contributions of the other. The variations in number and amplitude of these transitions determine the changes in intensity of the peak. Our results contribute to the understanding of electronic excitations in this systems along the $\Gamma K$ direction, which is the relevant direction for spectroscopic measurements. They also unveil the non-trivial relation between valley physics and excitonic dispersion in h--BN, opening the possibility to tune excitonic effects by playing with the interference between transitions. Furthermore, this study introduces analysis tools and a methodology that are completely general. They suggest a way to regroup independent-particle transitions which could permit a deeper understanding of excitonic properties in any system

Size dependent phase diagrams of Nickel-Carbon nanoparticles

The carbon rich phase diagrams of nickel-carbon nanoparticles, relevant to catalysis and catalytic chemical vapor deposition synthesis of carbon nanotubes, are calculated for system sizes up to about 3 nanometers (807 Ni atoms). A tight binding model for interatomic interactions drives the Grand Canonical Monte Carlo simulations used to locate solid, core/shell and liquid stability domains, as a function of size, temperature and carbon chemical potential or concentration. Melting is favored by carbon incorporation from the nanoparticle surface, resulting in a strong relative lowering of the eutectic temperature and a phase diagram topology different from the bulk one. This should be taken into account in our understanding of the nanotube growth mechanisms

A Tight-Binding Grand Canonical Monte Carlo Study of the Catalytic Growth of Carbon Nanotubes [Working paper]

The nucleation of carbon nanotubes on small nickel clusters is studied using a tight binding model coupled to grand canonical Monte Carlo simulations. This technique closely follows the conditions of the synthesis of carbon nanotubes by chemical vapor deposition. The possible formation of a carbon cap on the catalyst particle is studied as a function of the carbon chemical potential, for particles of different size, either crystalline or disordered. We show that these parameters strongly influence the structure of the cap/particle interface which in turn will have a strong effect on the control of the structure of the nanotube. In particular, we discuss the presence of carbon on surface or in subsurface layers

Excitons in few-layer hexagonal boron nitride: Davydov splitting and surface localization

Hexagonal boron nitride (hBN) has been attracting great attention because of its strong excitonic effects. Taking into account few-layer systems, we investigate theoretically the effects of the number of layers on quasiparticle energies, absorption spectra, and excitonic states, placing particular focus on the Davydov splitting of the lowest bound excitons. We describe how the inter-layer interaction as well as the variation in electronic screening as a function of layer number $N$ affects the electronic and optical properties. Using both \textit{ab initio} simulations and a tight-binding model for an effective Hamiltonian describing the excitons, we characterize in detail the symmetry of the excitonic wavefunctions and the selection rules for their coupling to incoming light. We show that for $N > 2$, one can distinguish between surface excitons that are mostly localized on the outer layers and inner excitons, leading to an asymmetry in the energy separation between split excitonic states. In particular, the bound surface excitons lie lower in energy than their inner counterparts. Additionally, this enables us to show how the layer thickness affects the shape of the absorption spectrum.Comment: 24 pages, 10 figure

Excitons in boron nitride single layer

Boron nitride single layer belongs to the family of 2D materials whose optical properties are currently receiving considerable attention. Strong excitonic effects have already been observed in the bulk and still stronger effects are predicted for single layers. We present here a detailed study of these properties by combining \textit{ab initio} calculations and a tight-binding-Wannier analysis in both real and reciprocal space. Due to the simplicity of the band structure with single valence ($\pi$) and conduction ($\pi^*$) bands the tight-binding analysis becomes quasi quantitative with only two adjustable parameters and provides tools for a detailed analysis of the exciton properties. Strong deviations from the usual hydrogenic model are evidenced. The ground state exciton is not a genuine Frenkel exciton, but a very localized "tightly-bound" one. The other ones are similar to those found in transition metal dichalcogenides and, although more localized, can be described within a Wannier-Mott scheme