Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

Ferreira, Aires; Viana-Gomes, José; Bludov, Yuliy V.; Pereira, Vitor M.; Peres, N. M. R.; Neto, A. H. Castro

doi:10.1103/physrevb.84.235410

Cited by 142 publications

(144 citation statements)

References 56 publications

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“…In Fig. 3 the 2D Ohm conductivity is plotted as a function of energy for fixed values of B = 7 × 10 4 G, chemical potential µ = 200 MeV and ǫ = 6.8 MeV, which are typical values for a graphenelike system [14] and [13]. The figure also shows the imaginary part of the conductivity.…”

Section: Quantum Faraday Effect For a Relativistic Fermion Gasmentioning

confidence: 99%

“…Let us suppose that the graphene plate is located at x 3 = 0 and the incoming electromagnetic wave is linearly polarized along the x 1 direction, and travels in the positive x 3 direction. Due to the optical Faraday rotation of the polarization vector when the wave crosses the graphene sheet, both the reflected and transmitted component acquire a component along the x 2 direction ( [13], [14], [26]). …”

Section: D+1 System: Faraday Effect and Rotation Faraday Anglementioning

confidence: 99%

“…51)-(52] must be multiplied by two, to account for the sublattice-valley degeneracy in graphene. The frequency must be substituted by ω → ω + iǫ where the imaginary part-ǫ is a phenomenological parameter associated with system disorder ( [13], [14]). In Fig.…”

Section: Quantum Faraday Effect For a Relativistic Fermion Gasmentioning

confidence: 99%

“…Our results for 2D+1 massless system are in agreement with previous theoretical work for FR in graphene reported in Refs. [12]- [14]. The 2D+1 results have been obtained from 3D+1 results by dimensional compactification.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, in quasiplanar condensed matter systems such as graphene (a genuine monolayer of carbon atoms in a honeycomb array, whose theoretical properties are essentially described by a twodimensional relativistic chiral fermion system [8]- [10]), FR is observed when light propagates perpendicular to the graphene layer in the presence of a static magnetic field with k B and the relation between the Faraday angle and the nonstatic (ω = 0) Hall conductivity has been pointed out [11]- [14].…”

Section: Introductionmentioning

confidence: 99%

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Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

Rodríguez¹,

Martı́nez²,

Rojas³

et al. 2013

Phys. Rev. A

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We study Faraday rotation in the quantum relativistic limit. Starting from the photon selfenergy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the fermion-antifermion gas is studied. The connection between Faraday Effect and Quantum Hall Effect (QHE) is discussed. The Faraday Effect is also investigated for a massless relativistic (2D+1)-dimensional fermion system which is derived by using the compactification along the dimension parallel to the magnetic field. The Faraday angle shows a quantized behavior as Hall conductivity in two and three dimensions.

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Section: Quantum Faraday Effect For a Relativistic Fermion Gasmentioning

confidence: 99%

Section: D+1 System: Faraday Effect and Rotation Faraday Anglementioning

confidence: 99%

Section: Quantum Faraday Effect For a Relativistic Fermion Gasmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

Rodríguez¹,

Martı́nez²,

Rojas³

et al. 2013

Phys. Rev. A

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Graphene: Manipulate Terahertz Waves

Zhou

Fan

et al. 2014

Graphene Optoelectronics

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Cavity‐Induced Enhancement of Magneto‐Optic Effects in Monolayer Transition Metal Dichalcogenides

Gao

et al. 2018

Advanced Optical Materials

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experimentally. [9][10][11][12][13][14] In addition, graphene allows the FR angles being controlled continuously by external parameters such as chemical potential or an external magnetic field, which is superior to that of conventional bulky magnetic materials always with fixed MO properties. Therefore, graphene opens up great possibilities for MO functionalities, such as optical isolators and one-way transmission devices based on 2D layered materials. [15,16] The successful exfoliation of monolayer transitional metal dichalcogenides (TMDC) inspires a broad exploration of optical and MO properties in related materials. [17][18][19][20][21][22][23][24][25][26][27][28][29][30] Monolayer TMDC family can be represented as the type of MX 2 (M = Mo, W, V and X = S, Se, or Te), in which M atoms are sandwiched between two planes of X atoms. The coexistence of broken inversion symmetry and strong spin-orbit coupling (SOC) of monolayer MX 2 makes them promising platforms for various valley-related properties, such as valley Hall effects as well as valley polarization. [18,20,21] It was known that the electronic structures of monolayer MoS 2 are protected by time reversal symmetry and thus there are no intrinsic magneto-optical effects in its pristine form. A key requirement for the generation of MO effects is to break time reversal symmetry, thus it is a promising way to apply an external magnetic field upon the system. [25][26][27][28] In this regard, there have been significant advancements in the MO effects of monolayer MX 2 . It has been reported that valley Zeeman splitting, polarization, and coherence of the excitonic valley pseudospin can be controlled by virtue of magnetic field, which have been observed in monolayer WSe 2 by performing polarization-resolved magnetophotoluminescence. [25] The possibility of producing a rotation of the emission polarization with respect to the excitation (the coherent superposition of valley states) has been confirmed in monolayer WS 2 (WSe 2 ), whose rotation angle can be up to 35° (30°) when the applied magnetic field reaches up to be 25 T (9 T). [29,30] These works establish the key steps toward understanding the intrinsic spin and valley properties of monolayer MX 2 .However, the above MO-related behaviors in monolayer MX 2 always require strong magnetic fields, severely restricting their realistic applications. The generation of MO effects in monolayer MX 2 will be particularly interesting if there is no need of magnetic field, as that would allow 2D layered materials in more practical positions for the realization of MO devices.Monolayer transition metal dichalcogenides represent a class of 2D directbandgap semiconductors, which do not support magneto-optical (MO) effects in the absence of magnetic field due to time reversal symmetry. Magnetic exchange field (MEF) has been demonstrated to be able to generate MO effects in monolayer transition metal dichalcogenides, causing Faraday rotation of several tenths of degree without the need of magnetic field. Here, the possibility of...

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Faraday effect in graphene enclosed in an optical cavity and the equation of motion method for the study of magneto-optical transport in solids

Cited by 142 publications

References 56 publications

Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

Quantized Faraday effect in (3+1)-dimensional and (2+1)-dimensional systems

Graphene: Manipulate Terahertz Waves

Cavity‐Induced Enhancement of Magneto‐Optic Effects in Monolayer Transition Metal Dichalcogenides

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