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

TL;DR

This study investigates the long-range effects of substitutional nitrogen dopants in graphene using DFT and tight-binding models, revealing how supercell size influences defect properties and enabling analysis of isolated impurities.

Contribution

It introduces a method combining DFT and tight-binding models to study nitrogen doping effects and defect interactions in graphene, addressing supercell size convergence issues.

Findings

Supercell size significantly affects local density of states around N defects.

Tight-binding models can simulate isolated N impurities and random distributions.

Calculated STM images match experimental observations.

Abstract

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.