Raman Tensor Research Articles

Optical Effect Modulation in Polarized Raman Spectroscopy of Transparent Layered α-MoO3.

Optical anisotropy, which is quantified by birefringence (Δn) and linear dichroism (Δk), can significantly modulate the angle-resolved polarized Raman spectroscopy (ARPRS) response of anisotropic layered materials (ALMs) by external interference. This work studies the separate modulation of birefringence on the ARPRS response and the intrinsic response by selecting transparent birefringent crystal α-MoO3 as an excellent platform. It is found that there are several anomalous ARPRS responses in α-MoO3 that cannot be reproduced by the real Raman tensor widely used in non-absorbing materials; however, they can be well explained by considering the birefringence-induced Raman selection rules. Moreover, the systematic thickness-dependent study indicates that birefringence modulates the ARPRS response to render an interference pattern; however, the amplitude of modulation is considerably lower than that by linear dichroism as occurred in black phosphorous. This weak modulation brings convenience to the crystal orientation determination of transparent ALMs. Combining the atomic vibrational pattern and bond polarizability model, the intrinsic ARPRS response of α-MoO3 is analyzed, giving the physical origins of the Raman anisotropy. This study employs α-MoO3 as an example, although it is generally applicable to all transparent birefringent ALMs.

Phonon polarization deformation in graphene induced by substrate coupling strengths

Displacement in the Raman shift of conventional Raman spectroscopy usually includes an increase in the number of material layers or a strain variation. To distinguish them, polarization-resolved Raman spectroscopy provides an additional degree of freedom to resolve it. In this work, strained graphene induced by different substrates on G band and 2D band phonon modes is studied by polarization-resolved Raman spectroscopy and verified by numerical analysis using Raman tensors and optical Jones calculus. For the strained graphene case, polarization properties of scattered light are obviously different from that in the case of unstrained graphene. Deformation of phonon polarization is seen to originate from different strengths of substrate coupling. This research provides an efficient quantitative method to explore any distortion of strain anisotropy in two-dimensional materials, which is important for the development of straintronics in the future.

Orientation-polarization dependence of pressure-induced Raman anomalies in anisotropic 2D ReS2.

We report an in situ high-pressure (0-30.24 GPa) optical study of the 2D ReS2 crystal under four specific configurations of sample orientation and laser polarization. Unlike the horizontal measurement configuration that has been widely used, under the vertical sample configuration we observe the anomalous disappearance behavior of Raman modes. Through analyzing the peak evolution under different configurations with tensor calculations, we identify the effect of pressure on different components in the full 3 × 3 Raman tensor of the anisotropic ReS2 crystal. These results provide new evidence on the remarkable tunability of pressure engineering on the crystal structure, and our methods offer an additional degree of freedom for studying pressure engineering on 2D anisotropic materials.

Significantly anisotropic Raman response of the (110) surface in quasi-one-dimensional system (TaSe4)2I by polarized Raman spectroscopy.

Quasi-one-dimensional materials are usually characterized by optical response spectroscopy methods, which show significant polarization dependence. Herein, we report a systematical investigation of polarized Raman scattering on the (110) crystal surface of the layered (TaSe4)2I compound. Taking into account group theory analysis of the crystal structure and the Raman tensor transformation technique, the vibrational mode of the Raman peaks can be differentiated by the angular dependence of the Raman peak intensity in parallel and vertical polarization Raman scattering tests. Moreover, density functional perturbation theory (DFPT) calculation confirmed the form of the Raman tensor of the (110) crystal surface, which was consistent with the result of the Raman tensor transformation technique, and the Raman spectrum and phonon dispersion curve calculations were also performed based on the Vienna ab initio simulation package (VASP). This new method provides useful insight for accurately identifying the lattice vibration behavior in new 2D layered structures.

Raman microscopy tracks maturity of melanin intermediates in Botrytis cinerea, a plant pathogen.

We use Raman microscopy to describe the structure and chemical composition of both conidiophore and hyphae of Botrytis cinerea, a common plant pathogen. To interpret experimental data, we use density functional theory (DFT) to compute Raman tensors specific to an important fungal glycopeptide, a segment of α-chitin, and several naphthalene-based precursors of increasing complexity, which we propose play a role in the melanin synthesis pathway. Using spectral interpretations based on quantum chemical validation, we review microscopy images reconstructed for specific Raman activities and describe differences in distributions of structural components, photo-protective secondary naphthalene-based pigments, and proteins in both spores and hyphal filaments. Comparison of our results with literature data on other fungi suggests an example of convergent evolution expressed at the level of secondary metabolites specific to plant pathogenic fungi. Our results indicate that pre-resonant Raman monitoring of melanin precursors may help assessment of local Botrytis population biology to aid agricultural production.

Angle-Dependent Raman Scattering Studies on Anisotropic Properties of Crystalline Hexagonal 4H-SiC.

Raman scattering spectroscopy (RSS) has the merits of non-destructiveness, fast analysis, and identification of SiC polytype materials. By way of angle-dependent Raman scattering (ADRS), the isotropic characteristics are confirmed for c-face 4H-SiC, while the anisotropic properties of a-face 4H-SiC are revealed and studied in detail via combined experiments and theoretical calculation. The variation functional relationship of the angle between the incident laser polarization direction and the parallel (perpendicular) polarization direction was well established. The selection rules of wurtzite 4H-SiC are deduced, and the intensity variations of the A1, E2, and E1 Raman phonon modes dependent on the incident angle are calculated, and well-matched with experimental data. Raman tensor elements of various modes are determined.

Electric field enhancement effect on Raman spectra in two-dimensional MoSi[formula omitted]N[formula omitted], TiSi[formula omitted]N[formula omitted] and MoGe[formula omitted]As[formula omitted] monolayers

Characterizing two-dimensional (2D) layered materials in the monolayer limit is key to discovering their new phenomena and unusual properties. We theoretically predict the electric field modulated Raman spectra of 2D MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, with two kinds of laser lines (532 and 633 nm). Based on the Raman tensor, we have calculated the angle-dependent Raman intensities of the major Raman peak (A1′1) in MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, locating at 1029 cm−1, 993 cm−1 and 317 cm−1, respectively. Applying the external electric field to MoSi2N4 monolayer, the symmetry of D3h reduces to C3v, which results in more peaks of Raman-active modes found in the Raman spectra. As a result, besides E′ and A1′ modes, three other major Raman peaks (A1′1, A1′2 and A1′3) are found in MoSi2N4, TiSi2N4 and MoGe2As4 monolayers, which can help us to distinguish the 2D MA2Z4 materials. We find that the enhancement factor by external electric field can be up to 10 times. Moreover, the non-resonant Raman spectra peaks of doubly degenerate mode (E′) and one-dimensional modes A1′ and A2″ in MoSi2N4, TiSi2N4 and MoGe2As4 monolayer are calculated. These theoretical results of Raman spectra of MoSi2N4 monolayer may provide theoretical guidelines for its utilization in crystal structure characterizations and optoelectric devices.

Helicity exchange and symmetry breaking of in-plane phonon scattering of h-BN probed by polarized Raman spectroscopy

Due to its atomic thickness and insulating nature, hexagonal boron nitride (h-BN) is considered to be one of the most promising substrates and gate insulating materials for two-dimensional electronic devices. In this study, polarized Raman spectroscopy was employed to uncover the effects of polarized incident light on the optical properties of h-BN phonon modes. Our measured polarization-resolved Raman spectra indicate that the symmetrical nature and the broken symmetry of degenerate phonon modes from h-BN are induced by linearly and elliptically polarized light, respectively. Moreover, a helicity exchange was observed between the excitation of circularly polarized light and the resulting opposite circular polarization of scattered light from h-BN. The measured phenomena were modeled on the basis of Raman tensors and Jones calculus to eventually calculate the amplitude coefficients of two orthogonal in-plane phonon modes. Hence, our experimental study provides a holistic understanding of the vibrational modes in h-BN, which is expected to enhance the knowledge of physical mechanisms such as heat capacity and thermal and electrical conductivities of this layered material.

Structure, Thermodynamics, and Raman Spectroscopy of Rhenium-Doped Bulk MoS2 from First Principles

Doping MoS$_2$ with Re is known to alter the electronic, structural, and tribological properties. Re-doped MoS$_2$ has been previously mainly studied in monolayer or few-layer form, but can also be relevant for applications in many-layer or bulk form. In this work, we use density functional theory to explore the structure, phase stability, and Raman spectrum of bulk Re-doped MoS$_2$. We consider the possibility of the Re dopant existing at different locations and provide experimentally distinguishable characteristics of the most likely sites: Mo-substitution and tetrahedral (t-) intercalation. We demonstrate and benchmark a general approach to calculate Raman spectra of doped materials with metallic densities of states by using atomic Raman tensors from the pristine material. Applying this method to the metallic Re-doped structures, we find characteristic shifts in the Raman-active peaks depending on Re dopant position: redshifts in both A$_{\rm 1g}$ and E$_{\rm 2g}^1$ peaks in the t-intercalated case versus a redshift for A$_{\rm 1g}$ and blueshift (sometimes accompanied by a smaller redshifted peak) for E$_{\rm 2g}^1$ peaks in the Mo-substituted case, which can be used to identify the dopant sites in experimental samples. We analyze the interactions giving rise to these shifts.

Discerning the Vibrational Nature of ReS2 Raman Modes Using Solid-Angle-Resolved Raman Spectroscopy

ReS2 exhibits reduced crystal symmetry, which leads to pronounced anisotropy and intricate Raman vibrations. However, to date, the vibrational nature of ReS2 Raman modes has remained elusive, with unresolved theoretical disputes. Here, we study Raman vibrations in ReS2 crystals using solid-angle-resolved Raman spectroscopy, which allows us to leverage the full 3 × 3 Raman tensor to resolve the Ag-like and Eg-like nature of all the 18 Raman modes. Combined with pressure-dependent measurements, we observe distinct behavior in the Ag-like and Eg-like modes. Our findings show unambiguous experimental evidence for discerning the ReS2 Raman modes and can offer important insights into the vibrational nature of Raman modes in layered anisotropic crystals.

Polarized Raman spectroscopy on topological semimetal Co3Sn2S2

AbstractWe present polarized Raman spectroscopy of the topological semimetal Co3Sn2S2, which was recently shown to host a Weyl semimetal phase. Stokes Raman spectra were obtained with the incident light parallel to the c‐axis of Co3Sn2S2. Two major phonon Raman peaks were observed at 289 and 386 cm−1 over continuous background emission signals. The intensity of the low‐wavenumber (289 cm−1) peak showed no polarization dependence. The high‐wavenumber (386 cm−1) peak and the continuous background signal were strongly polarized in the incident light polarization direction. These responses were almost independent of the in‐plane crystal orientation to the incident polarization, as is the manifestation of the point group symmetry of the unit cell of Co3Sn2S2. According to the group theory and Raman tensor analyses, the low‐ and high‐wavenumber Raman signals are attributed to Γ point phonon modes with and symmetries, respectively. Furthermore, line shape analyses revealed that the high‐wavenumber mode exhibited asymmetric peak feature well described by the Breit–Wigner–Fano function. These results suggest the Fano resonance between the phonon scattering with the continuous electronic background associated with low energy excitations near the Fermi energy. The clarified phonon energies and symmetries, as well as the electronic contribution to the Raman scattering, will not only be useful as a fingerprint to readily verify the experimentally grown or theoretically calculated crystal structure but also suggest importance of Raman spectroscopy as an effective tool to study low energy excitations and their interactions in Co3Sn2S2.

Raman tensor studies on defective non-van der Waals Bi2O2Se

The Raman tensors of the three modes at ∼55, ∼80, and ∼160 cm−1 for the non-van der Waals layered material Bi2O2Se, which were assigned to Eu, Eg, and A1g, respectively, were experimentally investigated. Two modes at ∼55 and ∼80 cm−1, which were not observable in perfect crystal Bi2O2Se in the backscattering configuration, owing to the Raman selection rule, were activated by defects. These two modes exhibit strong polarization dependence at line defects and the excitation energy; thus, their Raman polarizability tensors exhibit strong dependence on the defect morphology and geometric characteristics of Bi2O2Se. The results of this study confirm that the Raman tensors of nanocrystalline structures can be modulated by defects.

Birefringence in the Polarized Raman Scattering of Biaxial van der Waals α‐MoO3

AbstractThe effect of birefringence in anisotropic materials has been a long‐term issue for polarized Raman scattering. In this work, the polarization‐dependent Raman scattering in anisotropically birefringent materials is modeled with birefringence considered in the fundamental polarization selection rule. The birefringence‐induced polarization transformation is treated as a tensor in the calculation of Raman scattering intensity. The validity of this theory is further demonstrated in experiments by taking angle‐resolved polarized Raman measurements on the basal and cross planes of α‐MoO3—a typical biaxial van der Waals crystal with strong in‐plane and out‐of‐plane anisotropy. The anomalous angular dependency of polarized Raman scattering intensity can be well reproduced by the modified theoretical model with fitted real‐valued Raman tensors and birefringence‐related parameters. It can be concluded that this work can provide a valuable reference and guidance for quantitative analyses of anisotropic materials by using polarization‐resolved Raman scattering spectroscopy.

Uncovering strong π-metal interactions on Ag and Au nanosurfaces under ambient conditions via in-situ surface-enhanced Raman spectroscopy

Uncovering strong π-metal interactions on Ag and Au nanosurfaces under ambient conditions via in-situ surface-enhanced Raman spectroscopy

Polarization-Resolved and Helicity-Resolved Raman Intensity of Monolayer and Bilayer β-InSe

The structural and vibrational properties along with the polarization-resolved and helicity-resolved Raman spectra of monolayer and bilayer β-InSe excited by two commonly used laser lines (532 and 633 nm) in experiments are investigated by first-principles calculations so that we can establish the correlation between layer stacks and optical features in two-dimensional InSe. The stability of both monolayer and bilayer InSe are examined and confirmed by phonon dispersion. The monolayer and bilayer InSe are found to exhibit different point group symmetries and thereby the Raman properties due to the symmetry breaking of bilayer structure caused by interlayer van der Waals interaction. All Raman-active modes for monolayer (bilayer) InSe are listed, and the polarization-angle-dependent Raman intensities are accordingly discussed separately in terms of the configuration of the incident light (parallel or perpendicular to certain planes). By calculating the Raman tensor of each Raman-active mode, we obtained polarization-angle-dependent Raman intensities and discussed the location of each maximum under different polarization configurations, as well as the nonpolarized Raman intensity. The helicity-resolved Raman intensity is also obtained. It is found that more Raman-active modes can be observed under helical excitation when the incident light wave vector is in the y-direction. Among all of the Raman-active modes, the Raman intensity of A′1(A1g) is the strongest. Our work might help material scientists to characterize monolayer and bilayer InSe in experiments.

First-principles calculations of double resonance Raman spectra for monolayer MoTe2

Since double resonance Raman (DRR) spectra are laser-energy dependent, the first-principles calculations of DRR for two-dimensional materials are challenging. Here, the DRR spectrum of monolayer MoTe$_2$ is calculated by home-made program, in which we combine {\em ab-initio} density-functional-theory calculations with the electron-phonon Wannier (EPW) method. Within the fourth-order perturbation theory, we are able to quantify not only the electron-photon matrix elements within the dipole approximation, but also the electron-phonon matrix elements using the Wannier functions. The reasonable agreement between the calculated and experimental Raman spectra is achieved, in which we reproduce some distinctive features of transition metal dichalcogenides (TMDCs) from graphene (for example, the dominant intervalley process involving an electron or a hole). Furthermore, we perform an analysis of the possible DRR modes over the Brillouin zone, highlighting the role of low-symmetry points. Raman tensors for some DRR modes are given by first principles calculations from which laser polarization dependence is obtained.

Epitaxial growth and polarized Raman scattering of niobium dioxide films

We report the structural, electrical, and optical characterization of epitaxial niobium dioxide (NbO2) films fabricated on MgF2(001) substrates. The films were almost stoichiometric, had an indirect bandgap of 0.7 eV, and exhibited a phase transition at ∼1080 K. A polarized Raman scattering study of the films was conducted to investigate the Raman symmetry in the low-temperature phase. Based on the angular-dependent polarized Raman spectra, we assigned 13 modes to Ag symmetry and 14 to Bg symmetry. We also evaluated the Raman tensor elements of the Bg modes and found that the off-diagonal elements were nearly zero in most of the Bg modes, except for a phonon mode at 267 cm−1. This study aids understanding of the lattice dynamics of NbO2, which plays a critical role in the phase transition.

Characterisation of optical phonons within epitaxial Ge2Sb2Te5/InAs(111) structures

Femto-second pump-probe and micro-Raman spectroscopy (RS) measurements have been made to identify optical phonons in Ge2Sb2Te5/InAs(111) and an InAs(111) substrate. A theory of transient stimulated Raman scattering (TSRS) incorporating the Raman tensor predicts which phonon modes may be observed in transient reflectance (R) and anisotropic reflectance (AR) pump-probe measurements, and how their amplitudes depend upon angles φ and θ that describe the orientation of the pump and probe beam electric fields within the sample plane. AR measurements of an InAs(111) substrate revealed the 6.5 THz T2 transverse optical phonon with amplitude proportional to sin(2(θ−φ)), as expected for both TSRS and the specular optical Kerr effect (SOKE), confirming that TSRS and SOKE are equivalent descriptions of the same phenomenon. The AR responses of Ge2Sb2Te5/InAs(111) revealed a single coherent optical phonon (COP) mode at about 3.4 THz with sin(2(θ−φ)) amplitude variation that confirms the T2-like character of the mode and hence the underlying cubic structure of the epilayer. This mode was also observed in the R measurement for one sample, with amplitude independent of φ and θ as predicted by TSRS theory. Both R and AR signals were heavily damped, which is attributed to dephasing of T2x, T2y and T2z modes that become non-degenerate due to structural distortions. RS measurements revealed three modes for Ge2Sb2Te5/InAs(111) and three modes for InAs(111). Taken together the TSRS and RS measurements provide rich information about optical phonons in the phase change material Ge2Sb2Te5 and the InAs(111) surface.

Raman Optical Activity of 1T-TaS2.

Measurements of optical activity can be readily performed in transparent matter by means of a rotation of transmitted light polarization. In the case of opaque bulk materials, such measurements cannot be performed, making it difficult to assess possible chiral properties. In this work, we present full angular polarization dependencies of the Raman modes of bulk 1T-TaS2, which has recently been suggested to have chiral properties after pulsed laser excitation. We found that a mechanical rotation of the sample does not alter polarization-resolved Raman spectra, which can only be explained by introducing an antisymmetric Raman tensor, frequently used to describe Raman optical activity (ROA). Raman spectra obtained under circularly polarized excitation demonstrate that 1T-TaS2 indeed shows ROA, providing strong evidence that 1T-TaS2 is chiral under the used conditions of laser excitation. Our results suggest that ROA may be used as a universal tool to study chiral properties of quantum materials.

Interference of optical phonons in diamond studied using femtosecond pulses of polarized near-infrared light

The phononic interference of optical phonons in diamond is studied via transient transmittance change measurements using the double pump–probe protocol with polarized pump pulses. With orthogonal-polarized pulses, the phonon amplitude is enhanced/suppressed if the second pump pulse is irradiated by a half-integer/integer multiple of the phonon period. This is contrary to the usual phononic interference (enhancement at integer multiples of the phonon period) observed when using parallel-polarized pulses. These observed results are well explained using a quantum-mechanical model in calculations involving the Raman tensor of the diamond lattice structure. The amplitude of the optical phonons generated via the off-diagonal term of Raman tensor is proportional to the product of the x- and y−components of the optical electric field. The phase of the phonon oscillations is dependent on the angle between the crystal orientation and the polarization of the pump pulse.