Chiral Gauge Theory for Graphene

Jackiw, R.; Pi, So‐Young

doi:10.1103/physrevlett.98.266402

Cited by 183 publications

(272 citation statements)

References 9 publications

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“…Planar Dirac fermions in the background of the Abrikosov-Nielsen-Olesen vortex [9,10] were studied in Ref. [11], and, recently, the results of this work have been used to consider the influence of the Kekulé distortion in the honeycomb lattice on the electronic properties of graphene [12,13]. The present paper deals with yet another aspect, and our purpose is to elucidate the role of topological defects in the graphene lattice.…”

Section: Introductionmentioning

confidence: 99%

Electronic properties of graphene with a topological defect

Sitenko

Власій

2007

Nuclear Physics B

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Various types of topological defects in graphene are considered in the framework of the continuum model for long-wavelength electronic excitations, which is based on the Dirac-Weyl equation. The condition for the electronic wave function is specified, and we show that a topological defect can be presented as a pseudomagnetic vortex at the apex of a graphitic nanocone; the flux of the vortex is related to the deficit angle of the cone. The cases of all possible types of pentagonal defects, as well as several types of heptagonal defects (with the numbers of heptagons up to three, and six), are analyzed. The density of states and the ground state charge are determined.

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Section: Introductionmentioning

confidence: 99%

Electronic properties of graphene with a topological defect

Sitenko

Власій

2007

Nuclear Physics B

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“…In this way, an explanation for the scenario of fractionally charged vortices with localized zero modes, as proposed in Ref. [4] has been provided. Ultimately, the description of corrugation as a gauge field have become an experimental reality after the observation that Landau levels can be realized in graphene due exclusively to strain Refs.…”

Section: Introductionmentioning

confidence: 99%

“…These topological defects comes from the substitution of a hexagon by, for example, a pentagon, and this disclination warps (strains) the graphene sheet. Disclinations are implemented at theoretical level as a vortex of a axial-vector gauge potential which couple to the charge carriers degrees of freedom in the very same way the gauge potential enters in the chiral gauge model for graphene [4]. In fact, the introduction of a chiral gauge field in the Dirac equation to describe frustration in fullerenes were reported much earlier [12].…”

Section: Introductionmentioning

confidence: 99%

“…In particular, we show that a vortex of a pseudomagnetic gauge field by itself binds zero-energy fermion states whose spinor structure reveals that the zeroenergy states are supported on only one of the triangular sublattices, in the same way as those presented in Refs. [1,4]. The breaking of the sublattice symmetry by the fermion zero modes implies into an induced fractional fermion charge which is proportional to the flux of the pseudomagnetic field.…”

Section: Introductionmentioning

confidence: 99%

“…Jackiw and Pi [4] have proposed a chiral gauge theory for graphene. They show that the system considered in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

Obispo

Hott

2014

Phys. Rev. B

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We show that fermion charge fractionalization can take place in a recently proposed chiral gauge model for graphene even in the absence of Kekulé distortion in the graphene honeycomb lattice. In this model, electrons couple in a chiral way to a pseudomagnetic field with a vortex profile in such a way that it can be used to describe the influences of topological defects, such as disclinations, on the electronic states. We also extend the model by adding the coupling of fermions to an external magnetic field and show that the fermion charge can be fractionalized by means of only gauge potentials. It is shown that the chiral fermion charge can also have fractional value. We also relate the fractionalization of the fermion charge to the parity anomaly in an extended quantum electrodynamics, which involves vector and axial-vector gauge fields.

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Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

et al. 2018

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The full spectrum of two-dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of the novel 2D materials, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in 2D materials. We extend the analytical methods developed in the context of 1+1 field theories to explore the effect of the Lorentz symmetry breaking in the charge carrier density of 2D materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. Our findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory.

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Chiral Gauge Theory for Graphene

Abstract: We construct a chiral gauge theory to describe fractionalization of fermions in graphene. Thereby we extend a recently proposed model, which relies on vortex formation. Our chiral gauge fields provide dynamics for the vortices and also couple to the fermions.

Cited by 183 publications

References 9 publications

Electronic properties of graphene with a topological defect

Electronic properties of graphene with a topological defect

Fractional fermion charges induced by axial-vector and vector gauge potentials and parity anomaly in planar graphenelike structures

Lorentz Violation and Topologically Trapped Fermions in 2+1 Dimensions

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