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1.7. Impurities in graphene 33new electronic and geometric features beyond those present in a p z tight-binding model. Inthe following, we shall address the experimental observation of a monovacancy in grapheneand also its basic electronic and magnetic properties.For graphene, several experiments have observed vacancies and more complex defects[59, 61–63]. Those experiments irradiate the sample for some time using a focused electronbeam. Similar to proton irradiation in graphite (as seen in Section 1.5.1) but now with asubnanometer spot (e.g. ∼ 1 − 3 Å). Vacancies can be created with atomic precision atpredefined positions. For instance, we show a sequence of HRTEM images taken at roomtemperature of a reconstructed monovacancy in a single-layer graphene in Figure 1.12 (a)-(c).The vacancy is observed by the formation of a pentagon-like bond (see Figure 1.12(b)). Aftera few seconds the missing atom is replaced by a mobile adatom on the graphene surface as isseen in Figure 1.12(c). The monovacancy reconstructs in a geometry of C s symmetry differentfrom the D 3h structure displayed in Figure 1.11(a). The D 3h vacancy undergoes a Jahn-Tellerdistortion. This effect is shown by first principles calculations [60] which predict an energylowering of about 0.20 eV, divided into two parts: (i) the in-plane and symmetry preservingdistortion with 0.09 eV, and (ii) the out-of-plane and symmetry lowering with 0.11 eV. Thereconstructed geometries are plotted in Figure 1.12(e)-(f). For the symmetric D 3h vacancy(Figure 1.12(d)), the bond length between the first nearest neighbour atoms to the vacancy andthe next-nearest neighbours is shortened to 1.37 Å while the nearest-neighbour bond length inperfect graphene is ∼ 1.42 Å. This distortion preserves the symmetry and lowers the energyby ∼0.09 eV. Other bond lengths are only slightly changed. For the ground-state C s , thedistortion forms a pentagon-like structure with a bond length of ∼2.1 Å.The bond formation that accompanies the symmetry lowering lowers the energy by ∼0.10eV. Atom 3 suffers an out-of-plane displacement. This can be explained because the pairedelectrons in the new bond between atoms 1 and 2 in Figure 1.12(e) repel the electron on theopposite atom 3, so that the easiest direction for moving is an out-of-plane displacement offew tenths of an Angstrom [60]. We show the spin density projection on the graphene surfacegenerated by the reconstructed monovacancy in Figure 1.12(g). Most of the spin momentof the vacancy (∼1.04 µ B ) is due to atom 3, with a resulting spin pattern that only followsapproximately the original bipartite character of the graphene lattice. The bipartite characteris actually broken by the 1 − 2 bond.Although this description of the monovacancy seems to be detailed, substantially, as wewill see in Chapter 5, this picture is still incomplete in order to fully understand the magnetismof monovacancies in graphene. There are more ingredients that determine the stability of spinsolutions in a vacancy and its interplay with the global structure can create novel effects.1.7 Impurities in grapheneTo exploit the unique electronic properties of graphene requires to understand the effects ofimpurities in this material. Impurities are inevitable sources of electron scattering left from theproduction process and they may limit electron transport in graphene to a substantial extent.However, apart from being just undesirable, impurities provide a powerful tool for controllingthe electronic properties of graphene. In solid state materials, a clear application of impuritystates is the doping of semiconductor. In addition, impurities in graphene allow us to addressfundamental questions: for instance, impurity states in this material are directly related to
34 Chapter 1. IntroductionFigure 1.13: (a) Geometry of a H atom chemisorbed on top of a C atom in graphene. (b) Spin density projectionaround the H atom. (c) The resulting density of states (DOS) for spin-up and spin-down states after the doping.The dashed line shows the DOS of the ideal graphene. Labels indicate the character of the defect states. (d)Structure of the full hydrogenated graphene monolayer, graphane, in the chair conformation. The panel showsthe hexagonal carbon network with carbon in the sp 3 hybridization. (e) Geometry of half-hydrogenated graphenemonolayer (graphone) that was predicted to display magnetic behaviour. (f) Band structure of graphane with aclear band gap. Adapted from Refs. [58, 64–67].
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148 Bibliography[128] R. K. Saini,
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