Graphene transparency in weak magnetic fields

Valenzuela, David; Hernández-Ortíz, Saúl; Loewe, M.; Raya, Alfredo

doi:10.1088/1751-8113/48/6/065402

Cited by 16 publications

(23 citation statements)

References 45 publications

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“…These formulas are in agreement with results obtained in [49]. Since fermions are massless, dimensionless factors eB/ p 2 are built with | p| in place of m.…”

Section: Vacuum Polarization By a Constant Uniform Magnetic Field In supporting

confidence: 88%

Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

Khalilov

Mamsurov

2015

Eur. Phys. J. C

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The polarization operator (tensor) for planar charged fermions in a constant uniform magnetic field is calculated in the one-loop approximation of 2 + 1-dimensional quantum electrodynamics (QED 2+1 ) with a nonzero fermion density. We construct the Green function of the Dirac equation with a constant uniform external magnetic field in QED 2+1 at a finite chemical potential, find the imaginary part of this Green function, and then obtain the polarization tensor related to the combined contribution from real particles occupying the finite number of energy levels and magnetic field. We expect that some physical effects under consideration seem likely to be revealed in a monolayer graphene sample in the presence of an external constant uniform magnetic field B perpendicular to it.

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“…These formulas are in agreement with results obtained in [49]. Since fermions are massless, dimensionless factors eB/ p 2 are built with | p| in place of m.…”

Section: Vacuum Polarization By a Constant Uniform Magnetic Field In supporting

confidence: 88%

Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

Khalilov

Mamsurov

2015

Eur. Phys. J. C

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“…where the one-loop fermion self-energy and fermionphoton vertex were defined in Eqs. (31). Because Π µν (q) is gauge independent, all calculation can be carried out in a specific gauge.…”

Section: Two-loop Polarization Operatormentioning

confidence: 99%

“…with the one-loop polarization operator, fermion selfenergy and fermion-photon vertex defined in Eqs. (31). All calculations done, the general expression for the 2-loop photon self-energy diagrams of QED dγ ,de read:…”

Section: Two-loop Fermion Self-energymentioning

confidence: 99%

“…[25], QED dγ ,de was advocated as a minimal model to study the infra-red Lorentz invariant fixed point of Dirac liquids with a special focus on QED 4,3 relevant to intrinsic (or undoped) disorder-free graphene and similar planar materials. In the last years, there has been an increasing number of studies focusing on reduced QED and in particular QED 4,3 in relation with, e.g., transport and spectral properties [26][27][28][29], see also the short review [30], optical properties [31,32], quantum Hall effect [20,33,34] and dynamical chiral symmetry breaking [35,36] in planar systems. Moreover, QED 4,3 was shown to be unitary [37], its properties under the Landau-Khalatnikov-Frandkin transformation were studied [38], its precise relation to QED 3 understood [35], it was shown to possess a strong-weak duality mapping the coupling constant e toẽ = 8π/e with a self-dual point at e 2 = 8π (or α = 2) [39] and, even more recently, it has been studied as an interacting boundary conformal field theory [40].…”

Section: Introductionmentioning

confidence: 99%

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Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids

Teber

Kotikov

2018

Phys. Rev. D

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The field theoretic renormalization study of reduced quantum electrodynamics (QED) is performed up to two loops. In the condensed matter context, reduced QED constitutes a very natural effective relativistic field theory describing (planar) Dirac liquids, e.g., graphene and graphenelike materials, the surface states of some topological insulators, and possibly half-filled fractional quantum Hall systems. From the field theory point of view, the model involves an effective (reduced) gauge field propagating with a fractional power of the d'Alembertian in marked contrast with usual QEDs. The use of the Bogoliubov-ParasiukHepp-Zimmermann prescription allows for a simple and clear understanding of the structure of the model. In particular, in relation with the ultrarelativistic limit of graphene, we straightforwardly recover the results for both the interaction correction to the optical conductivity C Ã ¼ ð92 − 9π 2 Þ=ð18πÞ and the anomalous dimension of the fermion field γ ψ ðᾱ; ξÞ ¼ 2ᾱð1 − 3ξÞ=3 − 16ðζ 2 N F þ 4=27Þᾱ 2 þ Oðᾱ 3 Þ, whereᾱ ¼ e 2 =ð4πÞ 2 and ξ is the gauge-fixing parameter.

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“…Surprising results are coming also from magnetooptical experiments in mono and multilayer graphene [14]- [19], including the unexpectedly large Faraday rotation effect, which motivated both further experimental searches and theoretical studies [20]- [25].…”

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confidence: 99%

Minimum light transmission in graphene in the presence of a magnetic field

Esposito¹

2015

Mater. Res. Express

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We show that, on general theoretical grounds, transmission of light in graphene always presents a non-vanishing minimum value independently of any material and physical condition, the transmission coefficient being higher in the presence of a substrate, and getting increasing when QED corrections higher than α come into play. Explicit numerical calculations for typical cases are carried out when an external magnetic field is applied to the sample, showing that, in epitaxial graphene, a threshold effect exists leading to a non trivial minimum transmission, for a non vanishing light frequency, only for field values larger than a critical one, both in the large and in the intermediate chemical potential regime. Such a threshold effect manifests even in the maximum Faraday rotation polarization of light, which is substantially controlled by the applied magnetic field. Instead, more transmission minima in suspended graphene enters in the considered light frequency region for increasing magnetic field, displaying an effective shift of frequency bands where the sample gets more or less absorptive with a suitable tuning of the external field. Two transition regions in different magnetic field ranges are found, where the shift effect towards higher frequency values occurs both in the transmission coefficient and in the Faraday rotation angle. Potential technological application of the results presented are envisaged.The naturally-occurring single sheet of carbon atoms in graphene [1] has attracted considerable interest in the last decade in different areas of research and technology [2]-[5], due to the peculiar and particularly intriguing properties of such 2D material. Its hardness, yet flexibility, indeed, as well as high electron mobility and thermal conductivity, has put graphene in the spotlight of applied research in condensed matter physics. Also, the simple theoretical description [6] -confirmed by experimental evidences [7] -has showed that the properties of charge carriers in graphene are completely similar to those of ultrarelativistic electrons [8], the corresponding quasiparticles obeying a linear dispersion relation, so that a new era of Dirac materials has opened with potential applications in nanotechnology.Particularly extraordinary are the optical properties of monolayer graphene which, despite being only one atom thick, presents a surprisingly huge effect of absorption of a significant 2.3% fraction of the incident light [9], as a consequence of its unique conical electronic band structure [8]. This is just the behavior expected for ideal Dirac fermions [10]- [13], and the result proved to be valid for a wide range of frequencies. Graphene's opacity 1 − T πα 2.3% can be indeed obtained by calculating the absorption of light by two-dimensional Dirac particles with Fermi's golden rule, and its only dependence on the fine structure function α is a consequence of the fact that the optical conductivity σ = πe 2 /2h (e and h being the electron charge and the Planck constant, respectively) is independent of a...

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Graphene transparency in weak magnetic fields

Cited by 16 publications

References 45 publications

Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

Polarization operator in the 2+1 dimensional quantum electrodynamics with a nonzero fermion density in a constant uniform magnetic field

Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultrarelativistic limit of Dirac liquids

Minimum light transmission in graphene in the presence of a magnetic field

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