Electronic properties of curved graphene sheets

Abstract

A model is proposed to study the electronic structure of slightly curved graphene sheets with an arbitrary number of pentagon-heptagon pairs and Stone-Wales defects based on a cosmological analogy. The disorder induced by curvature produces characteristic patterns in the local density of states that can be observed in scanning tunnel and transmission electron microscopy.PACS numbers: 75.10. Jm, 75.10.Lp, 75.30.Ds The recent synthesis of single or few layers of graphite [1,2] allows to test the singular transport properties predicted in early theoretical studies [3,4,5,6] and experiments [7]. The discovery of a substantial field effect [8] and of ferromagnetic behavior [9] allows to envisage graphene as a reasonable replacement of nanotubes in electronic applications. Disorder plays a very important role in the electronic properties of low dimensional materials.Substitution of an hexagon by an n-sided ring in the hexagonal lattice without affecting the threefold coordination of the carbon atoms leads to the warping of the graphene sheet. Rings with n > 6 (n < 6), induce locally positive (negative) curvature. Inclusion of an equal number of pentagons and heptagonal rings would keep the flatness of the sheet at large scales and produce a flat structure with curved portions that would be structurally stable and have distinct electronic properties. This defects give rise to long range modifications in the electronic wave function that affect the electronics in a way different from that produced by vacancies or other impurities modelled by local potentials. Pentagon-heptagon pairs and Stone-Wales defects made of two adjacent heptagons and two pentagons form naturally in experiments of ion bombarded nanotubes as a mechanism to reduce the dangling bonds in large vacancies [10] and have been observed to form in situ in single graphene layers by highresolution transmission electron microscopy (TEM) [11].We propose a method, based on a cosmological analogy, to compute the electronic structure and transport properties of curved graphene sheets consisting of an arbitrary number of topological defects located at fixed positions of the lattice. We see that, unlike vacancies and voids, the combination of positive and negative curvature gives rise to characteristic inhomogeneous patterns in the density of states that affect the transport properties of the layers and can be observed in scanning tunnel (STM) and electron transmission spectroscopy (ETS). The present analysis can help in the experimental characterization of graphene samples and in the correct analysis of STM images. The results obtained can be related to recent Electrostatic Force Microscopy (EFM) measurements that indicate large potential differences between micrometer large regions on the surface of highly oriented graphite [12] and to the suppression of magnetorresistance in single layered graphene reported in [13]. We apply the formalism to present the corrections to the local density of states induced by pentagon-heptagon pairs and Stone-Wales defects in the...

A hydrothermal anvil made of graphene nanobubbles on diamond

“…In contrast, orbitals at the inner surface of the GNB (Fig. 4a) are rotated inwards to result in a diminished electron cloud, thus resulting in reduced reactivity of concaved graphene surface 39 .…”

Renormalization group aspects of graphene

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Optomechanical Analogy for Toy Cosmology with Quantized Scale Factor

“…Equation (20) reduces to Equation (13) when N = k = 1. Assume that the metric is approximately static between emissions and between measurements.…”

“…In addition, experiments with Bose-Einstein condensates (BEC) have demonstrated an analogy to Hawking radiation found with black holes [18]. Other analogies consider emulating the space-time, such as with BEC [19], graphene impurities [20], and in an optical lattice [21]. Recently, there was a proposal to emulate an FRW cosmology with circuit-QED using SQUIDS [22].…”