Raman selection rules in uniaxial media: The nonpolar modes of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Mn</mml:mi><mml:msub><mml:mi mathvariant="normal">Ga</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">Se</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

Alonso-Gutiérrez, P.; Sanjuán, M. L.; Morón, M. C.

doi:10.1103/physrevb.71.085205

Cited by 11 publications

(10 citation statements)

References 21 publications

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“…For the isotropic layered materials such as graphene, h‐BN, and MoS 2 , e i equals the polarization vectors of the electric fields for the incident light. However, for the anisotropic materials with high birefringence, the actual e i that interacts with the material is very different from the original polarization vector of the incident light due to the birefringence phenomenon. Similarly, the scattered light also suffers from the birefringence effect when it exits from the crystal.…”

Section: Resultsmentioning

confidence: 99%

“…However, for crystals with low symmetry, the polarization of both the incident laser and Raman‐scattered light can be exclusively altered due to the birefringence effect of the crystal itself, so that the polarized Raman scattering always deviates significantly from the normal Raman selection rule . Even though this abnormal polarized Raman behavior of the anisotropic crystals has been observed for many years,[3a,b,4] the influence of optical birefringence on the Raman selection rules of the anisotropic crystal itself has been rarely investigated even up to now. The key limitations are attributed to its considerable complexity with multitudinous influence factors for bulk crystals, such as the uncontrollable thickness, the uncertainty of the laser penetration depth, as well as the anisotropic absorption and reflection of the incoming and scattered light.…”

Section: Introductionmentioning

confidence: 99%

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Birefringence‐Directed Raman Selection Rules in 2D Black Phosphorus Crystals

Mao

Han

et al. 2016

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The incident and scattered light engaged in the Raman scattering process of low symmetry crystals always suffer from the birefringence-induced depolarization. Therefore, for anisotropic crystals, the classical Raman selection rules should be corrected by taking the birefringence effect into consideration. The appearance of the 2D anisotropic materials provides an excellent platform to explore the birefringence-directed Raman selection rules, due to its controllable thickness at the nanoscale that greatly simplifies the situation comparing with bulk materials. Herein, a theoretical and experimental investigation on the birefringence-directed Raman selection rules in the anisotropic black phosphorus (BP) crystals is presented. The abnormal angle-dependent polarized Raman scattering of the Ag modes in thin BP crystal, which deviates from the normal Raman selection rules, is successfully interpreted by the theoretical model based on birefringence. It is further confirmed by the examination of different Raman modes using different laser lines and BP samples of different thicknesses.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Birefringence‐Directed Raman Selection Rules in 2D Black Phosphorus Crystals

Mao

Han

et al. 2016

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“…In contrast, the second model considers the change of electric field vectors of the incident and scattered light due to the optical birefringence and linear dichroism of the anisotropic crystal . The polarizations of the incident and scattered light involved in the Raman scattering of biaxial BP crystals suffer from the influence of the birefringence and linear dichroism of BP.…”

Section: Raman Selection Rule For Phonons In Anisotropic Bp Crystalmentioning

confidence: 99%

Lattice Vibration and Raman Scattering in Anisotropic Black Phosphorus Crystals

Mao

Zhang

et al. 2018

Small Methods

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have reached 4000-6000 cm 2 V −1 s −1 . [1d,3] In addition, BP is among the few lessknown 2D layered crystals with direct bandgaps in both monolayer and multilayer forms. [1d,f,m,4] Owing to its strong interlayer interaction, BP exhibits extraordinary layer-dependent electronic structures with bandgaps varying from infrared (0.35 eV) to visible region (1.73 eV). [1h,m] Unlike most other well-studied layered crystals with isotropic in-plane lattice, BP has an anisotropic puckered structure that is stiff along one of the in-plane directions (zigzag) but flexible along the other (armchair). [1d] As a result, BP has shown significant anisotropy in electrical, optical, mechanical, and thermal properties. [1d,f,g,4b,5] In addition, BP has shown anisotropic electron and phonon dispersion, which give rises to the anisotropic electron-photon and electronphonon interactions. [1d,f,5f,6] Considering all of these properties, BP is a promising candidate for fieldeffect transistors, broad-band polarization-dependent photodetectors, and optical modulators. [1a,b,i,j,7] Raman spectroscopy is a fast and nondestructive characterization tool that provides structural and chemical information of materials. Even though they have a small effective scattering cross section, most nanomaterials show considerable Raman signal due to resonance effects and interference enhancement. [8] In recent years, Raman spectroscopy has demonstrated its powerful capability in characterizing 2D layered materials. Taking graphene as an example, Raman spectroscopy has revealed rich information on the chemical and electronic structure of graphene: the layer number and stacking order, the type of edges, the doping type, disorder and defects, and the interlayer interactions. [9] In addition, Raman spectroscopy has also been used to probe the electron-photon and electronphonon interactions in the Brillouin zone center, and to investigate the basic physicochemical properties such as the thermal conductivity. [9e,10] Here, we highlight the recent advances in the Raman scattering studies of 2D BP crystals. First, we introduce the basic concept of the atomic structure and discuss the crystal symmetry, lattice vibration, phonon dispersion, and layer-number dependence of the Raman spectra of BP. Then, we emphasize the anisotropic electron-photon and electron-phonon interactions in the orthorhombic BP crystal and review recent studies of the anomalous polarized Raman scattering in BP and its dependence on the excitation energy, thickness, and Here, an overview of recent advances on the Raman spectroscopic studies of 2D black phosphorus (BP) crystals is provided, covering the fundamentals of Raman scattering such as the crystal symmetry and the assignment of the phonon modes, the Raman selection rule that can be used to determine the crystalline orientation, the interlayer coupling that gives rise to the interlayer shear and breathing modes, and the effects of perturbation such as temperature, strain, and pressure. Due to the low in-plane symmetry of BP, ...

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“…A more detailed analysis would have to consider the change in the Raman-scattered intensities of the observed modes under the implicit dephasing effects of extraordinary light propagation in a uniaxial medium, rather than only the change in mode frequencies. 24 Nonetheless, any birefringence is of interest because it potentially allows for bulk phase-matching conditions to be reached in nonlinear optical processes, 25 which is not possible for a cubic crystal.…”

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Polarized zone-center phonon modes of wurtzite GaAs

et al. 2010

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Zone-center optical phonons are studied via polarized micro-Raman scattering in wurtzite GaAs crystals grown on sapphire. Polarized spectra reveal the A 1 -E 1 splitting in the Raman spectra of all polar optical modes of the wurtzite crystal. The polar mode splitting can be used to estimate a material birefringence of ⌬n ϳ 0.02.Driven by the substantial interest in producing technologies based on semiconductor structures with reduced dimensionality, researchers in recent years have dedicated significant effort to synthesizing semiconductor nanowires with a variety of growth methods. 1-3 From a materials perspective, one intriguing aspect of nanowire growth is the stability of a wurtzite crystalline phase of standard III-V semiconductors such as InP and GaAs, which in their planar forms always adopt a zincblende crystal structure. This dual stability results in the unanticipated challenge of producing single crystals during the growth process, as well as in necessitating characterization of these new forms of otherwise well-known semiconductors. While wurtzite-zincblende polytypism is known for III-nitride semiconductors, 4 among the IIIarsenides and III-phosphides it is unique to the nanoscale under ambient temperature and pressure conditions. 5 For understanding exhibited linear and nonlinear optical properties, modeling behavior, or designing devices upon the nanostructures in which the wurtzite modification appears, its bulk material characterization is of both fundamental and applied interest. We recently reported GaAs needles grown on silicon displaying tips sharp to a few-atom level of ϳ2-5 nm, 6,7 from which transmission electron microscope ͑TEM͒ analysis indicates a wurtzite crystalline structure entirely without twinned zincblende sections. Here, we focus on the vibrational properties of wurtzite GaAs, of especial interest for the very fundamental relationship of Raman scattering efficiencies to electro-optic and nonlinear coefficients of the material. 8,9 The atomic stacking sequence along the ͓111͔ direction of a zincblende crystal ͑staggered ABCABC͒ compared to the ͓0001͔ direction of the wurtzite crystal ͑eclipsed ABAB͒ results in the former being cubic ͑isotropic͒, while the latter is hexagonal ͑anisotropic͒ with characteristic c-axis and a-axes. The crystalline anisotropy necessitates a careful consideration of polarization dependences in experimental geometries with respect to the wurtzite optical axis ͑i.e., the c axis͒. The L͑ZB͒ → ⌫͑WZ͒ Brillouin zone-folding relationship 10 of the zincblende ͓111͔ to the wurtzite ͓0001͔ implies additional phonon modes at the center of the wurtzite Brillouin zone, which could also be expected simply considering the additional atoms present in the four-atom wurtzite primitive cell compared to the two atoms of the zincblende. 11 In order to elucidate the character of individual wurtzite phonon modes, here we concentrate on first-order Raman scattering, which by momentum considerations probes only processes occurring nearly at the center of the Brillouin zone. Wur...

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Raman selection rules in uniaxial media: The nonpolar modes ofMnGa2Se4

Cited by 11 publications

References 21 publications

Birefringence‐Directed Raman Selection Rules in 2D Black Phosphorus Crystals

Birefringence‐Directed Raman Selection Rules in 2D Black Phosphorus Crystals

Lattice Vibration and Raman Scattering in Anisotropic Black Phosphorus Crystals

Polarized zone-center phonon modes of wurtzite GaAs

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