Symmetry breaking perturbations in an electronically conducting medium are known to produce Friedel oscillations in various physical quantities of an otherwise pristine material. Here we show in a mathematically transparent fashion that Friedel oscillations in graphene have a strong sublattice asymmetry. As a result, the presence of impurities and/or defects may impact the distinct graphene sublattices very differently. Furthermore, such an asymmetry can be used to explain the recent observations that nitrogen atoms and dimers are not randomly distributed in graphene but prefer to occupy one of its two distinct sublattices. We argue that this feature is not exclusive of nitrogen and that it can be seen with other substitutional dopants.

Motivated by the recently observed sublattice asymmetry of substitutional nitrogen impurities in CVD grown graphene, we show, in a mathematically transparent manner, that oscillations in the local density of states driven by the presence of substitutional impurities are responsible for breaking the sublattice symmetry. While these oscillations are normally averaged out in the case of randomly dispersed impurities, in graphene they have either the same, or very nearly the same, periodicity as the lattice. As a result, the total interaction energy of randomly distributed impurities embedded in the conduction-electron-filled medium does not vanish and is lowered when their configuration is sublattice-asymmetric. We also identify the presence of a critical concentration of nitrogen above which one should expect the sublattice asymmetry to disappear. This feature is not particular to nitrogen dopants, but should be present in other impurities. * jalawlor@tcd.ie

SummaryIn this review we highlight recent theoretical and experimental work on sublattice asymmetric doping of impurities in graphene, with a focus on substitutional nitrogen dopants. It is well known that one current limitation of graphene in regards to its use in electronics is that in its ordinary state it exhibits no band gap. By doping one of its two sublattices preferentially it is possible to not only open such a gap, which can furthermore be tuned through control of the dopant concentration, but in theory produce quasi-ballistic transport of electrons in the undoped sublattice, both important qualities for any graphene device to be used competetively in future technology. We outline current experimental techniques for synthesis of such graphene monolayers and detail theoretical efforts to explain the mechanisms responsible for the effect, before suggesting future research directions in this nascent field.

Renowned for its sensitivity to detect the presence of numerous substances, graphene is an excellent chemical sensor. Unfortunately, which general features a dopant must have in order to enter the list of substances detectable by graphene are not exactly known. Here we demonstrate with a simple model calculation implemented in three different ways that one of such features is the symmetry properties of the impurity binding to graphene. In particular, we show that electronic scattering is suppressed when dopants are bound symmetrically to both graphene sub-lattices, giving rise to impurity invisibility. In contrast, dopants that affect the two sublattices asymmetrically are more strongly scattered and therefore the most likely candidates to being chemically sensed by graphene. Furthermore, we demonstrate that impurity invisibility is lifted with the introduction of a symmetry-breaking perturbation such as uniaxial strain. In this case, graphene with sublatticesymmetric dopants will function as efficient strain sensors. We argue that by classifying dopants through their bonding symmetry leads to a more efficient way of identifying suitable components for graphene-based sensors.

Recent experimental observations have reported that, rather than randomly distributed, nitrogen atoms may prefer to be located on one of the two sub-lattices of graphene. It has been suggested that such a preference may present a possible avenue to tailor the band gap of graphene whilst maintaining its excellent electronic transport properties. Among the proposed mechanisms to explain this effect is the suggestion that long-range inter-impurity interactions mediated by the conduction electrons of graphene may give rise to the asymmetry between sub-lattice occupations. Electron-mediated interactions are known to be prevalent not only between N atoms but also between impurities that are adsorbed to a specific location within the hexagonal structure, namely to the top of the carbon atom. Furthermore, this interaction is known to become more long-ranged as the dimensionality of the system is lowered. For that reason, in this paper we investigate whether a similar sublattice asymmetry appears in the case of metallic carbon nanotubes doped with Hydrogen adatoms. Our results indicate that similar sub-lattice asymmetries are observable and even more pronounced in small-diameter CNTs with a dilute concentration of adsorbates, diminishing with increasing diameter or impurity concentrations.