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

Cortijo, Alberto; Vozmediano, María A. H.

doi:10.1016/j.nuclphysb.2008.09.006

Cited by 63 publications

(93 citation statements)

References 34 publications

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“…However, in real experiments (like that of graphene) a 2 + 1 system may present structural defects [11]. These kind of defects can be modeled by considering field theories in curved spaces like spheres and cones and may also modify the electronic and transport properties of the system (see for instance [12,13]). …”

Section: U(n) × U(n)mentioning

confidence: 99%

A conical deficit in the AdS ₄ /CFT ₃ correspondence

Ballon-Bayona¹,

Ferreira²,

Otoya³

2010

Class. Quantum Grav.

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Inspired by the AdS/CFT correspondence we propose a new duality that allow the study of strongly coupled field theories living in a 2 + 1 conical space-time. Solving the 4-d Einstein equations in the presence of an infinite static string and negative cosmological constant we obtain a conical AdS 4 space-time whose boundary is identified with the 2 + 1 cone found by Deser, Jackiw and 't Hooft. Using the AdS 4 /CF T 3 correspondence we calculate retarded Green's functions of scalar operators living in the cone.

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Section: U(n) × U(n)mentioning

confidence: 99%

A conical deficit in the AdS ₄ /CFT ₃ correspondence

Ballon-Bayona¹,

Ferreira²,

Otoya³

2010

Class. Quantum Grav.

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“…We claim that the nonrelativistic results obtained in this contribution can be used to investigated the scalar Aharonov-Bohm effect in condensed matter systems. It is well known that topological defects similar to cosmic strings can be observed in condensed matter systems [57,60,70]. In this way, we can use these results to investigate the phase shift associated with quasiparticles with a constant magnetic moment by disclination in solids.…”

Section: Discussionmentioning

confidence: 94%

Scalar Aharonov‐Bohm effect in the presence of a topological defect

Bakke

Furtado²

2010

Annalen der Physik

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In this paper we study the scalar Aharonov-Bohm effect for a neutral particle possessing a magnetic dipole moment in the presence of a cosmic string. We study the phase shift acquired by the wave function of the neutral particle in the presence of this topological defect, investigate this phase shift within nonrelativistic and relativistic quantum descriptions considering two distinct magnetic field configurations and find that the scalar Aharonov-Bohm effect is composed by two contributions, with the first one arises due to the interaction of a magnetic dipole with an external field, and other one arises due to the presence of the cosmic string. The nondispersivity of this effect is also discussed.

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“…However, concerning the unique features found via TB calculations, only the feature of the Halperin-type edge states with an enhanced density spectrum (D2 region) maintains also in the continuum spectra; the rest of the special reczag features [see (III), (IV), and (VI) above] are missing in the continuum-DW spectrum. Due to this major discrepancy between the TB and continuum descriptions, we are led to conclude that the linearized DW equation fails to capture essential nonlinear physics (i.e., a nonlinear dispersion of energy versus momentum 54 coexisting with the Dirac cone), resulting from the introduction of a nontrivial (multiple) topological defect [55][56][57][58][59] (e.g., reconstructed reczag edge) in the honeycomb graphene lattice.…”

Section: Main Findingsmentioning

confidence: 99%

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

2012

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Systematic tight-binding investigations of the electronic spectra (as a function of the magnetic field) are presented for trigonal graphene nanoflakes with reconstructed zigzag edges, where a succession of pentagons and heptagons, that is 5-7 defects, replaces the hexagons at the zigzag edge. For nanoflakes with such reczag defective edges, emphasis is placed on topological aspects and connections underlying the patterns dominating these spectra. The electronic spectra of trigonal graphene nanoflakes with reczag edge terminations exhibit certain unique features, in addition to those that are well known to appear for graphene dots with zigzag edge termination. These unique features include breaking of the particle-hole symmetry, and they are associated with nonlinear dispersion of the energy as a function of momentum, which may be interpreted as nonrelativistic behavior. The general topological features shared with the zigzag flakes include the appearance of energy gaps at zero and low magnetic fields due to finite size, the formation of relativistic Landau levels at high magnetic fields, and the presence between the Landau levels of edge states (the socalled Halperin states) associated with the integer quantum Hall effect. Topological regimes, unique to the reczag nanoflakes, appear within a stripe of negative energies ε b < ε < 0, and along a separate feature forming a constant-energy line outside this stripe. The ε b lower bound specifying the energy stripe is independent of size.Prominent among the patterns within the ε b < ε < 0 energy stripe is the formation of threemember braid bands, similar to those present in the spectra of narrow graphene nanorings; they are associated with Aharonov-Bohm-type oscillations, i.e., the reczag edges along the three sides of the triangle behave like a nanoring (with the corners acting as scatterers) enclosing the magnetic flux through the entire area of the graphene flake. Another prominent feature within the ε b < ε < 0 energy stripe is a subregion of Halperin-type edge states of enhanced density immediately below the zero-Landau level. Furthermore, there are features resulting from localization of the Dirac quasiparticles at the corners of the polygonal flake.A main finding concerns the limited applicability of the continuous Dirac-Weyl equation, since the latter does not reproduce the special reczag features. Due to this discrepancy between the tightbinding and continuum descriptions, one is led to the conclusion that the linearized Dirac-Weyl equation fails to capture essential nonlinear physics resulting from the introduction of a multiple topological defect in the honeycomb graphene lattice.

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

Cited by 63 publications

References 34 publications

A conical deficit in the AdS ₄ /CFT ₃ correspondence

A conical deficit in the AdS ₄ /CFT ₃ correspondence

Scalar Aharonov‐Bohm effect in the presence of a topological defect

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

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

Cited by 63 publications

References 34 publications

A conical deficit in the AdS 4 /CFT 3 correspondence

A conical deficit in the AdS 4 /CFT 3 correspondence

Scalar Aharonov‐Bohm effect in the presence of a topological defect

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior

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A conical deficit in the AdS ₄ /CFT ₃ correspondence

A conical deficit in the AdS ₄ /CFT ₃ correspondence