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

Abstract

Being a true two-dimensional crystal, graphene has special properties. In particular, a point-like defect in graphene may induce perturbations in the long range. This characteristic 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 9 × 9 and 10 × 10 supercells. Although these calculations correspond to N concentrations that differ by ∼ 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 at% 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.

Inducing a Finite In-Plane Piezoelectricity in Graphene with Low Concentration of Inversion Symmetry-Breaking Defects

“…The different behavior of these two classes (multiples of 3 or not of the primitive cell of the pristine system) of graphene superlattices is now wellunderstood in terms of the energy band-folding model. [55][56][57] Indeed, even in pure graphene, when p is a multiple of 3, the two Dirac points K and K ′ in the primitive cell are folded to the Γ point of the hexagonal first-Brillouin zone (BZ) of the superlattice, giving rise to a fourfold degeneracy that can be broken, opening a band gap, by a periodic arrangement of defects. In the other case, the twofold degenerate Dirac points do not fold into Γ and a band gap opening can be induced by breaking the inversion symmetry.…”

Giant tunnel-electron injection in nitrogen-doped graphene

“…This extent corresponds to the typical size of the triangular pattern associated with a nitrogen atom in the STM images. Such a spatial extension also corresponds to the variation of the potential around a nitrogen atom [10]. The ratio between the conductance at the Fermi level above graphene (0.017 nS) and above nitrogen (9.15 nS) in Fig.…”

“…The nitrogen doping of graphene obtained by substitution of nitrogen atoms for carbon atoms is a suitable route to achieve well-controlled and well-characterized point defects with limited atomic relaxation [6][7][8] while preserving the band structure of graphene. At the atomic level, nitrogen doping induces a redistribution of the electron density on one sublattice and a localized resonance at nitrogen sites [8] that have been widely studied theoretically [10]. In this paper, we perform scanning tunneling spectroscopy (STS) experiments to study the local electron injection in nitrogen-doped graphene on SiC(0001).…”

Piezoelectricity of Functionalized Graphene: A Quantum-Mechanical Rationalization

“…By looking at the total values of the direct piezoelectric constant, it is seen that for small dopant concentrations the common asymptotic value of approximately 5×10 −10 C/m is reached for all systems, 21 Let us just briefly recall that this is due to the fact that the band gap of the system varies with defect concentration according to two distinct behaviors depending on whether the considered superlattice is or not a multiple of 3 of the primitive cell of pristine graphene, as predicted by the energy band-folding model. [52][53][54] As a further consideration, we might notice that the vibrational contribution is always smaller in absolute value than the electronic one, which is found to dominate the in-plane piezoelectric response of functionalized graphene.…”