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

Graphene, thanks to its extraordinary electronic and mechanical properties, is a potential candidate for a number of applications. Being one-atom thick, it is extremely sensitive to the presence of adsorbed atoms and molecules (either physisorbed or chemisorbed on the surface) 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. In this contribution we review that basic features of atomic-scale defects that can be useful for material design. After a brief introduction of the main properties determining the peculiar graphene electronic structure, namely bipartitism and hexagonal symmetry, we first focus on isolated “pz defects” such as atom vacancies or adsorbed species which covalently bind carbon atoms. In particular, we discuss in detail the formation of so-called midgap states [1,2] and the microscopically ordered magnetic structures which give rise to. Next we analyse the electronic structure of multiple defective graphene substrates, starting from the simplest situation where defects are randomly arranged. This is the case, for instance, of C atom vacancies which are usually obtained by irradiating samples with high energy beams of electrons or atoms. In particular, we show how it is possible to use simple rules to predict the presence of magnetic moments and midgap states by looking at the defect locations on the lattice. 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 a preferential sticking on specific lattice positions. This allows us to explain, for instance, why adsorption of H atoms does not occur randomly on graphene [3]. As a consequence, we conclude that formation of graphane by hydrogenation of graphene would be impossible if electronic effects were the only driving force. Then, we consider the reverse problem, that is how to use defects (vacancies, adsorbed species, substitutional dopants, etc..) to engineer graphene electronic properties. This is possible nowadays since recent advances in lithographic and self-assembling techniques allow one to produce well-ordered structures, e.g. superlattices of holes with defect diameter 2-3 nm long and lattice spacing 4-5 nm [4,5]. These superstructures allow one to control to some degree the electronic bands by means on few superlattice parameters, e.g. defects concentration and arrangement. In this context, using group theoretical arguments and electronic structure calculations, we show how it is possible to open a band-gap in graphene and preserve at the same time the pseudo-relativistic behaviour of its charge carriers. In particular, we show how arranging defects to form honeycomb-shaped superlattices (what we can call "supergraphenes") a gap opens in the band structure and new Dirac cones are created right close to the gapped region [6]. The induced-gaps are comparable in size to those found in nanoribbons at the same length scale. We further show how substitutional dopants, such as group IIIA/VA elements, when arranged to form analogous superlattices, show a gapped quasi-conical structure at the K point which gives rise to massive Dirac carriers. All these possible structures might find important technological applications in the development of novel graphene-based logic transistors. Indeed, current approaches to band-gap engineering usually fail to preserve the pseudo-relativistic behaviour of graphene electrons which is responsible for the high mobility of the charge carriers [7]. Finally, we briefly discuss molecular and metal doping, where simple chemical species physisorb on the surface and electron/hole dope it by electron transfer, leaving unaltered its basic electronic properties. This may be used to balance the shift of the Fermi level of those samples which are grown on a substrate, and which are electron/hole doped by the substrate itself. As substrate-grown samples are the natural candidates for wafer-scale production, this is an interesting issue towards fabrication of graphene-based devices. Recent experimental results show how it is possible to accurately adjust the Fermi level by such a molecular doping mechanism [8]. [1] M. Inui, S. A. Trugman, and E. Abrahams, “Unusual properties of midband states in systems with off-diagonal disorder”, Physical Review B 49, 3190 (1994). [2] V. M. Pereira, F. Guinea, J. M. B. Lopes dos Santos, N. M. R. Peres, and A. H. Castro Neto, “Disorder Induced Localized States in Graphene”, Physical Review Letters, 96, 036801 (2006) [3] S. Casolo, O. M. Lovvik, R. Martinazzo and G. F. Tantardini, “Understanding adsorption of hydrogen atoms on graphene”, Journal of Chemical Physics, 130, 054704 (2009) [4] J. C. Meyer, C. O. Girit, M. F. Crommie, and A. Zettl, “Hydrocarbon lithography on graphene membranes", Applied Physics Letters, 92, 123110 (2008) [5] J. Bai, X. Zhong, S. Jiang, Y. Huang, and X. Duan, “Graphene nanomesh”, Nature nanotechology 5, 190 (2010) [6] R. Martinazzo, S. Casolo and G.F. Tantardini, “Symmetry-induced band-gap opening in graphene superlattices”, in press on Physical Review B. Preprint at arXiv:0910.2407. [7] F. Schwierz, “Graphene transistors”, in press on Nature Nanotechology [8] C. 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