Band engineering in graphene with superlattices of substitutional defects

We investigate graphene superlattices of nitrogen and boron substitutional defects and by using symmetry arguments and electronic structure calculations we show how such superlattices can be used to modify graphene band structure. Specifically, depending on the superlattice symmetry, the structures considered here can either preserve the Dirac cones (D_{6h} superlattices) or open a band gap (D_{3h}). Relevant band parameters (carriers effective masses, group velocities and gaps, when present) are found to depend on the superlattice constant n as 1/n^{p} where p is in the range 1-2, depending on the case considered. Overall, the results presented here show how one can tune the graphene band structure to a great extent by modifying few superlattice parameters.Comment: accepted, J. Phys. Chem.

The effect of atomic-scale defects and dopants on graphene electronic structure

Graphene, being one-atom thick, is extremely sensitive to the presence of adsorbed atoms and molecules and, more generally, to defects such as vacancies, holes and/or substitutional dopants. This property, apart from being directly usable in molecular sensor devices, can also be employed to tune graphene electronic properties. Here we briefly review the basic features of atomic-scale defects that can be useful for material design. After a brief introduction on isolated $p_z$ defects, we analyse the electronic structure of multiple defective graphene substrates, and show how to predict the presence of microscopically ordered magnetic structures. Subsequently, we analyse the more complicated situation where the electronic structure, as modified by the presence of some defects, affects chemical reactivity of the substrate towards adsorption (chemisorption) of atomic/molecular species, leading to preferential sticking on specific lattice positions. Then, we consider the reverse problem, that is how to use defects to engineer graphene electronic properties. In this context, we show that arranging defects to form honeycomb-shaped superlattices (what we may call "supergraphenes") a sizeable gap opens in the band structure and new Dirac cones are created right close to the gapped region. Similarly, we show that substitutional dopants such as group IIIA/VA elements may have gapped quasi-conical structures corresponding to massive Dirac carriers. All these possible structures might find important technological applications in the development of graphene-based logic transistors.Comment: 16 pages, 14 figures, "Physics and Applications of Graphene - Theory" - Chapter 3, http://www.intechweb.org/books/show/title/physics-and-applications-of-graphene-theor

Symmetry-induced gap opening in graphene superlattices

We study nxn honeycomb superlattices of defects in graphene. The considered defects are missing p_z orbitals and can be realized by either introducing C atom vacancies or chemically binding simple atomic species at the given sites. Using symmetry arguments we show how it is possible to open a gap when n=3m+1,3m+2 (m integer), and estimate its value to have an approximate square-root dependence on the defect concentration x=1/n^2. Tight-binding calculations confirm these findings and show that the induced-gaps can be quite large, e.g. ~100 meV for x~10^{-3}. Gradient-corrected density functional theory calculations on a number of superlattices made by H atoms adsorbed on graphene are in good agreement with tight-binding results, thereby suggesting that the proposed structures may be used in practice to open a gap in graphene.Comment: 5 pages, 4 figure

Fighting the Curse of Dimensionality in First-Principles Semiclassical Calculations: Non-Local Reference States for Large Number of Dimensions

Semiclassical methods face numerical challenges as the dimensionality of the system increases. In the general context of the theory of differential equations, this is known as the “curse of dimensionality.” In the present manuscript, we apply the recently-introduced multi-coherent states semiclassical initial value representation (MC-SC-IVR) approach to extend the applicability of first-principles semiclassical calculations. The proposed strategy involves the use of non-local coherent states with the goal of increasing accuracy in the Fourier transforms, and on the other hand, allows for the selection of peaks of different frequencies. The ability to filter desired peaks is important for analyzing the power spectra of complex systems. The MC-SC-IVR approach allows us to solve a 19-dimensional test system and to resolve on-the-fly the power spectra of the formaldehyde molecule with very few classical trajectories.Chemistry and Chemical Biolog

First Principles Semiclassical Calculations of Vibrational Eigenfunctions

Vibrational eigenfunctions are calculated on-the-fly using semiclassical methods in conjunction with ab initio density functional theory classical trajectories. Various semiclassical approximations based on the time-dependent representation of the eigenfunctions are tested on an analytical potential describing the chemisorption of CO on Cu(100). Then, first principles semiclassical vibrational eigenfunctions are calculated for the $CO_2$ molecule and its accuracy evaluated. The multiple coherent states initial value representations semiclassical method recently developed by us has shown with only six ab initio trajectories to evaluate eigenvalues and eigenfunctions at the accuracy level of thousands trajectory semiclassical initial value representation simulations.Chemistry and Chemical Biolog

Understanding adsorption of hydrogen atoms on graphene

Adsorption of hydrogen atoms on a single graphite sheet (graphene) has been investigated by first-principles electronic structure means, employing plane-wave based, periodic density functional theory. A reasonably large 5x5 surface unit cell has been employed to study single and multiple adsorption of H atoms. Binding and barrier energies for sequential sticking have been computed for a number of configurations involving adsorption on top of carbon atoms. We find that binding energies per atom range from ~0.8 eV to ~1.9 eV, with barriers to sticking in the range 0.0-0.2 eV. In addition, depending on the number and location of adsorbed hydrogen atoms, we find that magnetic structures may form in which spin density localizes on a $\sqrt{3}{x}\sqrt{3}{R}30^{\circ}$ sublattice, and that binding (barrier) energies for sequential adsorption increase (decrease) linearly with the site-integrated magnetization. These results can be rationalized with the help of the valence-bond resonance theory of planar $\pi$ conjugated systems, and suggest that preferential sticking due to barrierless adsorption is limited to formation of hydrogen pairs.Comment: 12 pages, 8 figures and 4 table

Role of the self-interaction error in studying chemisorption on graphene from first-principles

Adsorption of gaseous species, and in particular of hydrogen atoms, on graphene is an important process for the chemistry of this material. At the equilibrium geometry, the H atom is covalently bonded to a carbon that puckers out from the surface plane. Nevertheless the \emph{flat} graphene geometry becomes important when considering the full sticking dynamics. Here we show how GGA-DFT predicts a wrong spin state for this geometry, namely $S_z$=0 for a single H atom on graphene. We show how this is caused by the self-interaction error since the system shows fractional electron occupations in the two bands closest to the Fermi energy. It is demonstrated how the use of hybrid functionals or the GGA+$U$ method an be used to retrieve the correct spin solution although the latter gives an incorrect potential energy curve

Atomic-scale characterization of nitrogen-doped graphite: Effects of dopant nitrogen on the local electronic structure of the surrounding carbon atoms

We report the local atomic and electronic structure of a nitrogen-doped graphite surface by scanning tunnelling microscopy, scanning tunnelling spectroscopy, X-ray photoelectron spectroscopy, and first-principles calculations. The nitrogen-doped graphite was prepared by nitrogen ion bombardment followed by thermal annealing. Two types of nitrogen species were identified at the atomic level: pyridinic-N (N bonded to two C nearest neighbours) and graphitic-N (N bonded to three C nearest neighbours). Distinct electronic states of localized {\pi} states were found to appear in the occupied and unoccupied regions near the Fermi level at the carbon atoms around pyridinic-N and graphitic-N species, respectively. The origin of these states is discussed based on the experimental results and theoretical simulations.Comment: 6 Pages, with larger figure

First-Principles Semiclassical Initial Value Representation Molecular Dynamics

A method for carrying out semiclassical initial value representation calculations using first-principles molecular dynamics (FP-SC-IVR) is presented. This method can extract the full vibrational power spectrum of carbon dioxide from a single trajectory providing numerical results that agree with experiment even for Fermi resonant states. The computational demands of the method are comparable to those of classical single-trajectory calculations, while describing uniquely quantum features such as the zero-point energy and Fermi resonances. By propagating the nuclear degrees of freedom using first-principles Born-Oppenheimer molecular dynamics, the stability of the method presented is improved considerably when compared to dynamics carried out using fitted potential energy surfaces and numerical derivatives.Comment: 5 pages, 2 figures, made stylistic and clarity change