Magneto-optical conductivity of anisotropic two-dimensional Dirac–Weyl materials

In this work, we construct coherent states for electrons in anisotropic 2D-Dirac materials immersed in a uniform magnetic field perpendicularly oriented to the sample. In order to describe the bidimensional effects on electron dynamics in a semiclassical approach, we adopt the symmetric gauge vector potential to describe the external magnetic field through a vector potential. By solving a Dirac-like equation with an anisotropic Fermi velocity, we identify two sets of scalar ladder operators that allow us to define generalized annihilation operators, which are generators of either the Heisenberg-Weyl or su(1, 1) algebra. We construct both bidimensional and su(1, 1) coherent states as eigenstates of such annihilation operators with complex eigenvalues. In order to illustrate the effects of the anisotropy on these states, we obtain their probability density and mean energy value. Depending upon the anisotropy, expressed by the ration between the Fermi velocities along the x-and y-axes, the shape of the probability density is modified on the xy-plane with respect to the isotropic case and according to the classical dynamics. * ediaz@fis.cinvestav.mx † moliva@fis.cinvestav.mx ‡ yconcha@umich.mx § raya@ifm.umich.mx arXiv:1907.06551v1 [quant-ph]

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“…As previous section, the states Φ mz τ (x, y) are obtained for the particular values η = 0 and γ = δ in Eq. (14).…”

Section: Su(11) Coherent States (Su(11)-cs)mentioning

confidence: 99%

Coherent states in magnetized anisotropic 2D Dirac materials

Díaz-Bautista¹,

Oliva-Leyva²,

Concha‐Sánchez³

et al. 2020

J. Phys. A: Math. Theor.

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“…[31][32][33] The most remarkable feature of these STS spectra is a series of well defined peaks at the Landau level energies, whose straininduced shifts can be correlated with the Fermi velocity variations. [31][32][33] In general, for a generic anisotropic Dirac material (8) in an external magnetic field B, its Landau levels are given by [34]…”

Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

“…Effects on Optical Measurements: Let us further explore the effect of Δ on the optical properties of strained graphene. As documented in Oliva-Leyva and Wang, [34] the optical response of an anisotropic Dirac material (8) can be expressed by the conductivity tensor,…”

Section: Effective Dirac Hamiltonianmentioning

confidence: 99%

“…The most remarkable feature of these STS spectra is a series of well defined peaks at the Landau level energies, whose strain‐induced shifts can be correlated with the Fermi velocity variations . In general, for a generic anisotropic Dirac material in an external magnetic field B , its Landau levels are given by

E_{n} = E_{n}^{true(0 true)} \sqrt{det true(true \overset{bold-italicυ}{true} / υ_{0} true)},

where

E_{n}^{true(0 true)}

correspond to those of an isotropic Dirac material. Replacing

true \bar{bold-italicυ}

into equation according to the expression , we arrive that the Landau level spectrum of strained graphene is,

E_{n} = E_{n}^{(0)} true[1 - (β - 1) tr (\bar{ε}) / 2 true],

which does not show dependence on κ .…”

mentioning

confidence: 99%

“…Effects on Optical Measurements : Let us further explore the effect of Δ on the optical properties of strained graphene. As documented in Oliva‐Leyva and Wang, the optical response of an anisotropic Dirac material can be expressed by the conductivity tensor,

\bar{σ} true(ω true) = {normalσ}_{0} true(ω true) true[\frac{normalt normalr (\bar{bold-italicυ})}{normaldet true(\overset{υ}{true} true)} \overset{υ}{true} - \overset{bold-italicI}{true} true],

where

σ_{0} true(ω true)

is the frequency‐dependent optical conductivity of the isotropic Dirac material with

\bar{υ} = υ_{0} \bar{I} .

Once again, making the substitution into equation of

\overset{υ}{true}

by expression , the optical conductivity tensor of strained graphene up to first order in the strain tensor

true \overset{bold-italicε}{true}

results,

\bar{σ} true(ω true) = σ_{0} true(ω true) true[true \overset{bold-italicI}{true} - 2 {β^{*}}^{} true \overset{bold-italicε}{true} + {β^{*}}^{} tr (\bar{ε})

…”

mentioning

confidence: 99%

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Wang

2018

Physica Rapid Research Ltrs

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The low‐energy electronic properties of strained graphene are usually obtained by transforming the bond vectors according to the Cauchy–Born rule. In this work, we derive a new effective Dirac Hamiltonian by assuming a more general transformation rule for the bond vectors under uniform strain, which takes into account the strain‐induced relative displacement between the two sublattices of graphene. Our analytical results show that the consideration of such relative displacement yields a qualitatively different Fermi velocity with respect to previous reports. Furthermore, from the derived Hamiltonian, we analyze effects of this relative displacement on the local density of states and the optical conductivity, as well as the implications on the scanning tunneling spectroscopy, including external magnetic field, and optical transmittance experiments of strained graphene.

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Advanced Materials and Device Architectures for Magnetooptical Spatial Light Modulators

Kharratian

Ürey

Onbaşlı

2019

Advanced Optical Materials

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Faraday and Kerr rotations are magnetooptical (MO) effects used for rotating the polarization of light in transmission and reflection from a magnetized medium, respectively. MO effects combined with intrinsically fast magnetization reversal, which can go down to a few tens of femtoseconds or less, can be applied in magnetooptical spatial light modulators (MOSLMs) promising for nonvolatile, ultrafast, and high‐resolution spatial modulation of light. With the recent progress in low‐power switching of magnetic and MO materials, MOSLMs may lead to major breakthroughs and benefit beyond state‐of‐the‐art holography, data storage, optical communications, heads‐up displays, virtual and augmented reality devices, and solid‐state light detection and ranging (LIDAR). In this study, the recent developments in the growth, processing, and engineering of advanced materials with high MO figures of merit for practical MOSLM devices are reviewed. The challenges with MOSLM functionalities including the intrinsic weakness of MO effect and large power requirement for switching are assessed. The suggested solutions are evaluated, different driving systems are investigated, and resulting device architectures are benchmarked. Finally, the research opportunities on MOSLMs for achieving integrated, high‐contrast, and low‐power devices are presented.

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Magneto-optical conductivity of anisotropic two-dimensional Dirac–Weyl materials

Cited by 19 publications

References 41 publications

Coherent states in magnetized anisotropic 2D Dirac materials

Coherent states in magnetized anisotropic 2D Dirac materials

Theory for Strained Graphene Beyond the Cauchy–Born Rule

Advanced Materials and Device Architectures for Magnetooptical Spatial Light Modulators

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