Charge Localization around Disclinations in Monolayer Graphite

Azevedo, S.; Furtado, C.; Moraes, Fernando

doi:10.1002/(sici)1521-3951(199806)207:2<387::aid-pssb387>3.0.co;2-0

Cited by 34 publications

(11 citation statements)

References 14 publications

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“…In this approach the defects are represented by metrics that are solutions of Einstein-Cartan equations in three space dimensions. An application of this model to graphite has appeared in [8], where localization of charge near heptagonal rings has been verified. In this geometrical background we analyze the global properties of the massless Dirac equation that describes the electronic spectrum of graphite at the Fermi level [9].…”

Section: Introductionmentioning

confidence: 99%

Geometric phases in graphitic cones

2008

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In this Letter we use a geometric approach to study geometric phases in graphitic cones. The spinor that describes the low energy states near the Fermi energy acquires a phase when transported around the apex of the cone, as found by a holonomy transformation. This topological result can be viewed as an analogue of the Aharonov-Bohm effect. The topological analysis is extended to a system with n cones, whose resulting configuration is described by an effective defect.

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Section: Introductionmentioning

confidence: 99%

Geometric phases in graphitic cones

2008

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“…The Schrödinger equation in the presence of dislocations was considered in for different problems. Problems related to the wave or Laplace equations were considered in [47][48][49][50][51][52][53][54]. The influence of the nontrivial metric related to the presence of defects was investigated in electrodynamics [55] and hydrodynamics [56].…”

Section: Introductionmentioning

confidence: 99%

Geometric theory of defects

Katanaev¹

2005

Usp. Fiz. Nauk

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A description of dislocations and disclinations defects in terms of RiemannCartan geometry is given, with the curvature and torsion tensors being interpreted as the surface densities of the Frank and Burgers vectors, respectively. A new free energy expression describing the static distribution of defects is presented, and equations of nonlinear elasticity theory are used to specify the coordinate system. Application of the Lorentz gauge leads to equations for the principal chiral SO(3)-field. In the defect-free case, the geometric model reduces to elasticity theory for the displacement vector field and to a principal chiral SO(3)-field model for the spin structure. As illustrated by the example of a wedge dislocation, elasticity theory reproduces only the linear approximation of the geometric theory of defects. It is shown that the equations of asymmetric elasticity theory for the Cosserat media can also be naturally incorporated into the geometric theory as the gauge conditions. As an application of the theory, phonon scattering on a wedge dislocation is considered. The energy spectrum of impurity in the field of a wedge dislocation is also discussed.

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“…A similar result has been obtained in [27] with numerical simulations. It is to note that a somehow contradictory result was obtained in [28] where they studied the electrostatics of a graphene plane with defects. They found that disclinations corresponding to rings with more (less) than six carbon atoms function as attractors (repellent) to point charges.…”

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confidence: 99%

Electronic properties of curved graphene sheets

2007

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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...

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Charge Localization around Disclinations in Monolayer Graphite

Cited by 34 publications

References 14 publications

Geometric phases in graphitic cones

Geometric phases in graphitic cones

Geometric theory of defects

Electronic properties of curved graphene sheets

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