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Register a new userPolarization analysis of first- and second-order Raman scattering from MoTe$_2$ single crystal
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We report on Raman experiments performed on a single crystal MoTe$_2$ sample. The system belongs to the wide family of Transition Metal Dichalcogenides which includes several of the most interesting two dimensional materials for both basic and applied physics. Measurements were performed in the standard basal plane configuration, by placing the $ab$ plane of the crystal perpendicular to the wave vector $k_i$ of the incident beam to explore the in plane vibrational modes, and in the edge plane configuration with $k_i$ perpendicular to the crystal $c$ axis, thus mainly exciting out-of-plane modes. For both configurations we performed a polarization-dependent Raman study and we were able to provide a complete assignment of the observed first- and second-order Raman peaks fully exploiting the polarization selection rules. Present findings are in complete agreement with previous first-order Raman data whereas a thorough analysis of the second-order Raman bands, either in basal- or edge-plane configurations, provides new information and a precise assignment of these spectral structures. In particular, we have observed Raman active modes of the $M$ point of the Brillouin zone previously predicted by ab-initio calculations and ascribed to either combination or overtone but never previously measured.
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We study the second-order Raman process of mono- and few-layer MoTe$_2$, by combining {em ab initio} density functional perturbation calculations with experimental Raman spectroscopy using 532, 633 and 785 nm excitation lasers. The calculated electronic band structure and the density of states show that the electron-photon resonance process occurs at the high-symmetry M point in the Brillouin zone, where a strong optical absorption occurs by a logarithmic Van-Hove singularity. Double resonance Raman scattering with inter-valley electron-phonon coupling connects two of the three inequivalent M points in the Brillouin zone, giving rise to second-order Raman peaks due to the M point phonons. The predicted frequencies of the second-order Raman peaks agree with the observed peak positions that cannot be assigned in terms of a first-order process. Our study attempts to supply a basic understanding of the second-order Raman process occurring in transition metal di-chalcogenides (TMDs) and may provide additional information both on the lattice dynamics and optical processes especially for TMDs with small energy band gaps such as MoTe$_2$ or at high laser excitation energy.
In this work, we carry out first-principles calculations and lattice mode analysis to investigate the polarization switching mechanism in HfO$_2$. Because the stability of the polar orthorhombic $Pca2_1$ phase of HfO$_2$ arises from a trilinear coupling, polarization switching requires the flipping of not only the polar $Gamma_{15}^Z$ mode, but also at least one zone-boundary anti-polar mode. The coupling between the polar and anti-polar modes thus leads to substantial differences among different polarization switching paths. Specifically, our lattice-mode-coupling analysis shows that paths in which the $X_2^-$ mode is reversed involve a large activation energy, which because the $X_2^-$ mode is nonpolar cannot be directly overcome by applying an electric field. Our results show that the anti-polar $Pbca$ phase, whose structure is locally quite similar to that of the $Pca2_1$ phase, similarly cannot be transformed to this phase by an electric field as this would require local reversal of the $X_2^-$ mode pattern. Moreover, for the domain wall structure most widely considered, propagation also requires the reversal of the $X_2^-$ mode, leading to a much larger activation energy compared with that for the propagation of domain wall structures with a single sign for the $X_2^-$ mode. Finally, these first-principles results for domain wall propagation in HfO$_2$ have implications to many experimental observations, such as sluggish domain wall motion and robust ferroelectricity in thin films, and lattice mode analysis deepens our understanding of these distinctive properties of ferroelectric HfO$_2$.
We present an textit{ab initio} study based on density-functional theory of first- and second-order Raman spectra of graphene-based materials with different stacking arrangements and numbers of layers. Going from monolayer and bilayer graphene to periodic graphitic structures, we investigate the behavior of the first-order G-band and of the second-order 2D-band excited by the same set of photon energies. The former turns out to be very similar in all considered graphene-based materials, while in the latter we find the signatures of individual structures. With a systematic analysis of the second-order Raman spectra at varying frenquency of the incident radiation, we monitor the Raman signal and identify the contributions from different phonon modes that are characteristic of each specific arrangement. Supported by good agreement with experimental findings and with previous theoretical studies based on alternative approaches, our results propose an effective tool to probe and analyze the fingerprints of graphene-based and other low-dimensional materials.
Resonant Raman spectra of single layer WS$_{2}$ flakes are presented. A second order Raman peak (2LA) appears under resonant excitation with a separation from the E$^{1}_{2g}$ mode of only $4$cm$^{-1}$. Depending on the intensity ratio and the respective line widths of these two peaks, any analysis which neglects the presence of the 2LA mode can lead to an inaccurate estimation of the position of the E$^{1}_{2g}$ mode, leading to a potentially incorrect assignment for the number of layers. Our results show that the intensity of the 2LA mode strongly depends on the angle between the linear polarization of the excitation and detection, a parameter which is neglected in many Raman studies.
We report two new first-order Raman modes in the spectra of few-layer MoS$_2$ at 286~cm$^{-1}$ and 471~cm$^{-1}$ for excitation energies above 2.4~eV. These modes appear only in few-layer MoS$_2$; therefore their absence provides an easy and accurate method to identify single-layer MoS$_2$. We show that these modes are related to phonons that are not observed in the single layer due to their symmetry. Each of these phonons leads to several nearly degenerate phonons in few-layer samples. The nearly degenerate phonons in few-layer materials belong to two different symmetry representations, showing opposite behavior under inversion or horizontal reflection. As a result, Raman active phonons exist in few-layer materials that have nearly the same frequency as the symmetry forbidden phonon of the single layer. We provide here a general treatment of this effect for all few-layer two-dimensional crystal structures with an inversion center or a mirror plane parallel to the layers. We show that always nearly degenerate phonon modes of different symmetry must occur and, as a result, similar pseudo-activation effects can be excepted.
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