Geometric phases in graphitic cones

Furtado, C.; Moraes, Fernando; Carvalho, Alexandre M. de M.

doi:10.1016/j.physleta.2008.06.029

Cited by 104 publications

(85 citation statements)

References 26 publications

(40 reference statements)

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“…A geometric formulation of the same problem has been given recently in [31] in terms of holonomy. In the case of an odd-membered ring, the two Fermi points are also exchanged [27] what can be modelled by using a non-abelian gauge potential that rotates the spinors in the SU (2) space of the Fermi points.…”

Section: Effect Of a Single Disclinationmentioning

confidence: 99%

Erratum to: “Effects of topological defects and local curvature on the electronic properties of planar graphene” [Nucl. Phys. B 763 (2007) 293–308]

Cortijo

Vozmediano

2009

Nuclear Physics B

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A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon-heptagon pairs and Stone-Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.

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Section: Effect Of a Single Disclinationmentioning

confidence: 99%

Erratum to: “Effects of topological defects and local curvature on the electronic properties of planar graphene” [Nucl. Phys. B 763 (2007) 293–308]

Cortijo

Vozmediano

2009

Nuclear Physics B

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“…At the apex of the graphitic cone the hexagon of the planar graphene lattice is replaced by a polygon having 6 − N c sites. The periodicity conditions for the combined bispinor = (ψ + , ψ − ) under the rotation around the cone apex are discussed in [76][77][78][79]. For even values of N c these conditions do not mix the spinors ψ + and ψ − , and we can apply the formulas given above.…”

Section: Expectation Values In Parity and Time-reversal Symmetric Modelsmentioning

confidence: 99%

Finite temperature fermion condensate, charge and current densities in a ( $$2+1$$ 2 + 1 )-dimensional conical space

et al. 2016

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We evaluate the fermion condensate and the expectation values of the charge and current densities for a massive fermionic field in (2 + 1)-dimensional conical spacetime with a magnetic flux located at the cone apex. The consideration is done for both irreducible representations of the Clifford algebra. The expectation values are decomposed into the vacuum expectation values and contributions coming from particles and antiparticles. All these contributions are periodic functions of the magnetic flux with the period equal to the flux quantum. Related to the non-invariance of the model under the parity and time-reversal transformations, the fermion condensate and the charge density have indefinite parity with respect to the change of the signs of the magnetic flux and chemical potential. The expectation value of the radial current density vanishes. The azimuthal current density is the same for both the irreducible representations of the Clifford algebra. It is an odd function of the magnetic flux and an even function of the chemical potential. The behavior of the expectation values in various asymptotic regions of the parameters are discussed in detail. In particular, we show that for points near the cone apex the vacuum parts dominate. For a massless field with zero chemical potential the fermion condensate and charge density vanish. Simple expressions are derived for the part in the total charge induced by the planar angle deficit and magnetic flux. Combining the results for separate irreducible representations, we also consider the fermion condensate, charge and current densities in parity and time-reversal symmetric models. Possible applications to graphitic nanocones are discussed. a

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“…In Ref. [32], one of us has used the parallel transport to investigated geometric phase in graphene by using the geometric theory of defects. When we transport a spinor Ψ around of defect in a graphene layer with a defect, we obtain…”

Section: Graphene: a Brief Reviewmentioning

confidence: 99%

“…The general expression of the parallel transport of a spinor around the apex of the cone in a graphene layer is given by a unitary transformation called holonomy [32,34].…”

Section: Graphene: a Brief Reviewmentioning

confidence: 99%

A Kaluza–Klein description of geometric phases in graphene

2012

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In this paper, we use the Kaluza-Klein approach to describe topological defects in a graphene layer. Using this approach, we propose a geometric model allowing to discuss the quantum flux in K-spin subspace. Within this model, the graphene layer with a topological defect is described by a four-dimensional metric, where the deformation produced by the topological defect is introduced via the three-dimensional part of metric tensor, while an Abelian gauge field is introduced via an extra dimension. We use this new geometric model to discuss the arising of topological quantum phases in a graphene layer with a topological defect.

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Geometric phases in graphitic cones

Cited by 104 publications

References 26 publications

Erratum to: “Effects of topological defects and local curvature on the electronic properties of planar graphene” [Nucl. Phys. B 763 (2007) 293–308]

Erratum to: “Effects of topological defects and local curvature on the electronic properties of planar graphene” [Nucl. Phys. B 763 (2007) 293–308]

Finite temperature fermion condensate, charge and current densities in a ( $$2+1$$ 2 + 1 )-dimensional conical space

A Kaluza–Klein description of geometric phases in graphene

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