Holding promising applications in power electronics, the wide band gap material gallium oxide has emerged as a vital alternative to materials like GaN and SiC. The detailed study of phonon modes in $β$-Ga$_{2}$O$_{3}$ provides insights into fundamental material properties such as crystal structure and orientation and can contribute to the identification of dopants and point defects. We investigate the Raman active phonon modes of $β$-Ga$_{2}$O$_{3}$ in two different oxygen isotope compositions ($^{16}$O,$^{18}$O) by experiment and theory: By carrying out polarized micro-Raman spectroscopy measurements on the (010) and ($\bar{2}$01) planes, we determine the frequencies of all 15 Raman active phonons for both isotopologues. The measured frequencies are compared with the results of density functional perturbation theory (DFPT) calculations. In both cases, we observe a shift of Raman frequencies towards lower energies upon substitution of $^{16}$O with $^{18}$O. By quantifying the relative frequency shifts of the individual Raman modes, we identify the atomistic origin of all modes (Ga-Ga, Ga-O or O-O) and present the first experimental confirmation of the theoretically calculated energy contributions of O lattice sites to Raman modes. We find that oxygen substitution on the O$_{\mathrm{II}}$ site leads to an elevated relative frequency shift compared to O$_{\mathrm{I}}$ and O$_{\mathrm{III}}$ sites. This study presents a blueprint for the future identification of different point defects in Ga$_{2}$O$_{3}$ by Raman spectroscopy.
Boron arsenide (c-BAs) is at the forefront of research on ultrahigh thermal conductivity materials. We present a Raman scattering study of isotopically tailored cubic boron arsenide single crystals for 11 isotopic compositions spanning the range from nearly pure c-$^{10}$BAs to nearly pure c-$^{11}$BAs. Our results provide insights on the effects of strong mass disorder on optical phonons and the appearance of two-mode behavior in the Raman spectra of mixed crystals. Strong isotope disorder also relaxes the one-phonon Raman selection rules, resulting in disorder-activated Raman scattering by a…
The current/voltage curve of metallic carbon nanotubes (CNTs) displays at high bias a sudden increase of the resistivity due to the scattering of electrons with phonons having an anomalously-high population (hot phonons). Here, we show that it is possible to improve the electrical performances of metallic CNTs by C13 isotope enrichment. In fact, isotopic disorder creates additional channels for the hot-phonon deexcitation, reduces their population and, thus, the nanotube high-bias differential-resistance. This is an extraordinary case where disorder improves the electronic transport.
The observation of the local - mode vibration, the two - mode behavior of the LO phonons at large isotope concentration, as well as large line broadening in LIH - D mixed crystals directly evidence strong additional phonon scattering due to the isotope - induced disorder.
The most important bands for the evaluation of strain in graphene (the 2D and 2D prime modes) are investigated. It is shown that for Bernal-stacked bilayers, the two-phonon Raman features have three different components that can be assigned to processes originating solely from the top graphene layer, bottom graphene layer, and from a combination of processes originating both from the top and bottom layers. The individual components of the 2D and 2D prime modes are disentangled. The reported results enable addressing the properties of individual graphene layers in isotopically labelled turbostr…
Lead sulfide is an important semiconductor that has found technological applications for over a century. Raman spectroscopy, a standard tool for the investigation and characterization of semiconductors, has limited application to this material because of the forbidden nature of its first order scattering and its opacity to visible lasers. Nevertheless, useful vibrational spectra from two-phonon processes are obtained with red lasers, probably because of a resonance in the concomitant electronic transitions. Here we report temperature dependent spectra, covering the 10-300 K range, for two samp…
The isotopic mass of constituent elements of materials has a well-known effect on the energy of vibrational modes. By means of monochromated scanning transmission electron microscopy we have experimentally studied the phonon bandstructure of hexagonal BN, where a phonon band gap appears between in-plane optical phonon modes and the lower energy part of the phonon spectrum. The size of the phonon band gap can be manipulated by the isotopic mass of the boron. While in $^{11}$BN the phonon band gap is about 7 meV wide, in $^{10}$BN the gap nearly closes, being an order of magnitude smaller (below…
We report an investigation of perovskite-type LaNiO3 thin films by Raman scattering in both various scattering configurations and as a function of temperature. The room-temperature Raman spectra and the associated phonon mode assignment provide reference data for phonon calculations and for the use of Raman scattering for structural investigations of LaNiO3, namely the effect of strain in thin films or heterostructures. The temperature-dependent Raman spectra from 80 to 900 K are characterized by the softening of the rotational A1g mode, which suggest a decreasing rhombohedral distortion towar…
Antiferromagnetic materials with strong spin-phonon coupling have the potential for spintronic applications. Here, we report the structural, magnetic, and vibrational properties of 12R-BaTi0.4Mn0.6O3. Temperature-dependent magnetization data show the presence of weak antiferromagnetic interactions. Correlation between magnetic and vibrational properties are probed by using temperature-dependent Raman spectroscopic measurements. Two of the Raman active phonons show deviation from anharmonic behaviour at low temperatures which can be attributed to spin-phonon coupling. The strength of coupling i…
We performed Raman spectroscopy measurements under temperature changes from 10 K up to 850 K to probe the phonon-spin coupling in Y$_2$NiMnO$_6$. The spin-phonon coupling was observed as a softening of the stretching mode, indicating this phonon stabilizes the magnetic interaction. The result indicates the rare earth ionic radius in Re$_2$NiMnO$_6$ double perovskites is not the unique parameter influencing the spin-coupling magnitude.
In ionic Raman scattering, infrared-active phonons mediate a scattering process that results in the creation or destruction of a Raman-active phonon. This mechanism relies on nonlinear interactions between phonons and has in recent years been associated with a variety of emergent lattice-driven phenomena in complex transition-metal oxides, but the underlying mechanism is often obscured by the presence of multiple coupled order parameters in play. Here, we use time-resolved spectroscopy to compare coherent phonons generated by ionic Raman scattering with those created by more conventional elect…
The semimetal NbIrTe4 has been proposed to be a Type-II Weyl semimetal with 8 pairs of opposite Chirality Weyl nodes which are very close to the Fermi energy. This topological electronic structure is made possible because of the broken inversion symmetry of NbIrTe4 which is an orthorhombic crystal with Td symmetry. Using micro-Raman scattering as a probe, we observe the frequencies and symmetries of 19 phonon modes (ranging from 40 to 260 cm-1) in this material and compare to Density Functional Theory calculations. Using angular and polarization resolved Raman scattering for green (514 nm) and…
We study the bulk and surface phonon-polaritons of the Zn0.67Be0.33Se zincblende alloy by near-forward Raman scattering. The short (Be-Se) bond exhibits a distinct percolation doublet in the conventional backscattering Raman spectra, corresponding to a three-mode behavior in total [1(Zn-Se),2(Be-Se)] for Zn0.67Be0.33Se. This offers an opportunity to achieve a refined understanding of the phonon-polariton modes of a zincblende alloy beyond the current two-mode approximation, corresponding to a [1(Zn-Se),1(Be-Se)] description in the present case. The discussion is supported by contour modeling o…
We use a combination of polarized Raman spectroscopy experiment and model magnetism-phonon coupling calculations to study the rich magneto-Raman effect in the two-dimensional (2D) magnet $\mathrm{CrI_3}$. We reveal a novel layered-magnetism-assisted phonon scattering mechanism below the magnetic onset temperature, whose Raman excitation breaks time-reversal symmetry, has an antisymmetric Raman tensor, and follows the magnetic phase transitions across critical magnetic fields, on top of the presence of the conventional phonon scattering with symmetric Raman tensors in $N$-layer $\mathrm{CrI_3}$…
We report a systematic investigation of orthorhombic perovskite-type RCrO3 powder samples by Raman scattering for nine different rare earth R3+ cations (R = Y, La, Pr, Sm, Gd, Dy, Ho, Yb, Lu). The room-temperature Raman spectra and the associated phonon mode assignment provide reference data for structural investigation of the whole series of RCrO3 orthochromites and phonon ab-initio calculations. The assignment of the chromite spectra and comparison with Raman data on other orthorhombic perovskites allows correlating the phonon modes with the structural distortions in the RCrO3 series. In par…
We present a systematic study of the Raman spectra of optical phonons in graphene monolayers under tunable uniaxial tensile stress. Both the G and 2D bands exhibit significant red shifts. The G band splits into two distinct sub-bands (G+, G-) because of the strain-induced symmetry breaking. Raman scattering from the G+ and G- bands shows a distinctive polarization dependence that reflects the angle between the axis of the stress and the underlying graphene crystal axes. Polarized Raman spectroscopy therefore constitutes a purely optical method for the determination of the crystallographic orie…
We have carried out temperature and pressure-dependent Raman and x-ray measurements on single crystals of Tb$_2$Ti$_2$O$_7$. We attribute the observed anomalous temperature dependence of phonons to phonon-phonon anharmonic interactions. The quasiharmonic and anharmonic contributions to the temperature-dependent changes in phonon frequencies are estimated quantitatively using mode Grüneisen parameters derived from pressure-dependent Raman experiments and bulk modulus from high pressure x-ray measurements. Further, our Raman and x-ray data suggest a subtle structural deformation of the pyrochlor…
Raman spectra obtained by the inelastic scattering of light by crystalline solids contain contributions from first-order vibrational processes (e.g. the emission or absorption of one phonon, a quantum of vibration) as well as higher-order processes with at least two phonons being involved. At second order, coupling with the entire phonon spectrum induces a response that may strongly depend on the excitation energy, and reflects complex processes more difficult to interpret. In particular, excitons (i.e. bound electron-hole pairs) may enhance the absorption and emission of light, and couple str…
It has long been puzzling regarding the atomistic origin of the pressure-induced Raman phonon stiffening that generally follows a polynomial expression with coefficients needing physical indication. Here we show that an extension of the bond-order-length-strength (BOLS) correlation mechanism to the pressure domain has led to an analytical solution to connect the pressure-induced Raman phonon stiffening directly to the bonding identities of the specimen and the response of the bonding identities to the applied stimulus. It is found that the pressure-induced blue-shift of Raman phonons arises fr…
In this letter we investigated the temperature-dependent Raman spectra of CaMn7O12 helimagnet from room temperature down to 10 K. The temperature dependence of the Raman mode parameters show remarkable anomalies for both antiferromagnetic and incommensurate transitions that this compound undergoes at low temperatures. The anomalies observed at the magnetic ordering transition indicate a spin-phonon coupling at higher-temperature magnetic transition in this material, while a magnetostrinction effect at the lower-temperature magnetic transition.
Recently, phonons with chirality (chiral phonons) have attracted significant attention. Chiral phonons exhibit angular and pseudo-angular momenta. In circularly polarized Raman spectroscopy, the peak split of the $Γ_3$ mode is detectable along the principal axis of the chiral crystal in the backscattering configuration. In addition, peak splitting occurs when the pseudo-angular momenta of the incident and scattered circularly polarized light are reversed. Until now, chiral phonons in binary crystals have been observed, whereas those in unary crystals have not been observed. Here, we observe ch…
Determination of acoustic phonon anharmonicities via second-order Raman scattering in CuI
Universität Leipzig（莱比锡大学）；Friedrich-Schiller-Universität Jena（耶拿弗里德里希·席勒大学）；Federal Institute for Materials Research and Testing（联邦材料研究与测试研究所）；Ruhr University Bochum（波鸿鲁尔大学）
We report the influence of Ni/Mn ordering on the spin-phonon coupling in multifunctional La2NiMnO6. Three types of films with different levels of structural order, including long-range Ni/Mn cation order, cation disorder, and an admixture of the ordered and disordered phases, are compared by polarized micro-Raman spectroscopy and magnetometry. Each film displays a strong dependence on the polarization configuration and a unique set of Raman active phonon excitations. Long-range cation ordering results in the splitting of Raman active phonon peaks because of Brillouin zone folding and lowering …
Gallium arsenide nanowires were synthesized by gallium-assisted molecular beam epitaxy. By varying the growth time, nanowires with diameters ranging from 30 to 160 nm were obtained. Raman spectra of the nanowires ensembles were measured. The small line width of the optical phonon modes agree with an excellent crystalline quality. A surface phonon mode was also revealed, as a shoulder at lower frequencies of the longitudinal optical mode. In agreement with the theory, the surface mode shifts to lower wave numbers when the diameter of the nanowires is decreased or the environment dielectric cons…
We have performed polarized Raman scattering measurements on WTe$_2$, for which an extremely large positive magnetoresistance has been reported recently. We observe 5 A$_1$ phonon modes and 2 A$_2$ phonon modes out of 33 Raman active modes, with frequencies in good accordance with first-principles calculations. The angular dependence of the intensity of the peaks observed is consistent with the Raman tensors of the $C_{2v}$ point group symmetry attributed to WTe$_2$. Although the phonon spectra suggest neither strong electron-phonon nor spin-phonon coupling, the intensity of the A$_1$ phonon m…
We perform a comparative experimental and theoretical study of the temperature dependence up to 700 K of the frequency and linewidths of the graphite E1u and E2g optical phonons (~1590 and 1580 cm-1) by infra-red (IR) and Raman spectroscopy. Despite their similar character, the temperature dependence of the two modes is quite different, being, e.g., the frequency shift of the IR-active E1u mode is almost twice as big as that of the Raman active E2g mode. Ab initio calculations of the anharmonic properties are in remarkable agreement with measurements and explain the observed behavior.
In this letter, we report that the special coupling between Dirac fermion and lattice vibrations, in other words, electron-phonon coupling (EPC), in silicene layers on Ag(111) surface was probed by an in-situ Raman spectroscopy. We find the EPC is significantly modulated due to tensile strain, which results from the lattice mismatch between silicene and the substrate, and the charge doping from the substrate. The special phonon modes corresponding to two-dimensional electron gas scattering at edge sites in the silicene were identified. Detecting relationship between EPC and Dirac fermion throu…
In stimulated Raman scattering, two incident optical waves induce a force oscillating at the difference of the two light frequencies. This process has enabled important applications such as the excitation and coherent control of phonons and magnons by femtosecond laser pulses. Here, we experimentally and theoretically demonstrate the so far neglected up-conversion counterpart of this process: THz sum-frequency excitation of a Raman-active phonon mode, which is tantamount to two-photon absorption by an optical transition between two adjacent vibrational levels. Coherent control of an optical la…
We present an analysis of deep-UV Raman measurements of graphite, graphene and carbon nanotubes. For excitation energies above the strong optical absorption peak at the $M$ point in the Brillouin zone ($\approx 4.7\,\text{eV}$), we partially suppress double-resonant scattering processes and observe the two-phonon density of states of carbon nanomaterials. The measured peaks are assigned to contributions from LO, TO, and LA phonon branches, supported by calculations of the phonon dispersion. Moreover, we gain access to the infrared-active $E_{1u}$ mode in graphite. By lowering the excitation en…
We investigate by near-forward Raman scattering a presumed reinforcement of the (A-C,B-C)-mixed phonon-polariton of a A1-xBxC zincblende alloy when entering its longitudinal optical (LO-)regime near the Brillouin zone centre Γ, as predicted within the formalism of the linear dielectric response. A choice system to address such issue is ZnSe0.68S0.32 due to the moderate dispersion of its refractive index in the visible range, a sine qua non condition to bring the phonon-polariton insight near Γ. The LO-regime is actually accessed by using the 633.0 nm laser excitation, testified by the strong e…
We employ a combined experimental-theoretical study of the first- and second-order Raman modes of monoclinic $β$-Ga$_{2}$O$_{3}$. The investigated materials is of particular interest due to its deep-UV bandgap paired with a high critical field strength, offering promising applications in power-electronics. A crucial prerequisite for the future development of Ga$_{2}$O$_{3}$-based devices is a detailed understanding of the lattice dynamics as they are important for the elasticity (through acoustic phonons), thermal conductivity (through the heat transferred by phonons), the temperature-dependen…
The symmetry group analysis is applied to classify the phonon modes of $N$-stacked graphene layers (NSGL's) with AB- and AA-stacking, particularly their infra-red and Raman properties. The dispersions of various phonon modes are calculated in a multi-layer vibrational model, which is generalized from the lattice vibrational potentials of graphene to including the inter-layer interactions in NSGL's. The experimentally reported red shift phenomena in the layer number dependence of the intra-layer optical C-C stretching mode frequencies are interpreted. An interesting low frequency inter-layer op…
We report a Raman spectroscopy study of graphene field-effect transistors (GFET) with a controlled amount of defects introduced in graphene by exposure to electron-beam irradiation. Raman spectra are taken at T = 8 K over a range of back gate voltages (Vg) for various irradiation dosages (Re). We study effects in the Raman spectra due to Vg-induced doping and artificially created disorder at various Re. With moderate disorder (irradiation), the Raman G peak with respect to the graphene carrier density (nFE) exhibits a minimum in peak frequency and a maximum in peak width near the charge- neutr…
2H-TaSe2 is a model transition metal dichalcogenide material that develops charge density waves (CDWs).Here we present variable-temperature Raman spectroscopy study on both incommensurate charge density waves (ICDW) and optical phonon modes of 2H-TaSe2 thin layers exfoliated onto SiO2 substrate. Raman scattering intensities of all modes reach a maximum when the sample thickness is about 11 nm. This phenomenon can be explained by optical interference effect between the sample and the substrate. The E2gICDW amplitude modes experience redshift as temperature increases. We extract ICDW transition …
Structural modifications in InP(111) due to 1.5 MeV implantation of Sb have been characterized using first order and second order Raman spectroscopy. With both Longitudinal Optical (LO) and Transverse Optical (TO) modes allowed for InP(111), we have investigated the evolution of both these modes as a function of fluence. Intensity, linewidth and shifts of the phonons, for both first order and second order Raman modes, display the increase in damage in the lattice with increasing fluence. The results suggest that the presence of a charge layer in the vicinity of the surface may be effecting the…
We report the existence of broad and weakly asymmetric features in the high-energy (G) Raman modes of freely suspended metallic carbon nanotubes of defined chiral index. A significant variation in peak width (from 12 cm-1 to 110 cm-1) is observed as a function of the nanotube's chiral structure. When the nanotubes are electrostatically gated, the peak widths decrease. The broadness of the Raman features is understood as the consequence of coupling of the phonon to electron-hole pairs, the strength of which varies with the nanotube chiral index and the position of the Fermi energy.
UV Raman scattering studies show longitudinal optical (LO) mode up to 4th order in wurtzite GaN nanowire system. Frohlich interaction of electron with the long range electrostatic field of ionic bonded GaN gives rise to enhancement in LO phonon modes. Good crystalline quality, as indicated by the crystallographic as well as luminescence studies, is thought to be responsible for this significant observation. Calculated size dependence, incorporating size corrected dielectric constants, of electron-phonon interaction energy agrees well with measured values and also predict stronger interaction e…
Molybdenum disulfide (MoS$_2$) is a promising material for making two-dimensional crystals and flexible electronic and optoelectronic devices at the nanoscale. MoS$_2$ flakes can show high mobilities and have even been integrated in nanocircuits . A fundamental requirement for such use is efficient thermal transport. Electronic transport generates heat which needs to be evacuated, more crucially so in nanostructures. Anharmonic phonon-phonon scattering is the dominant intrinsic limitation to thermal transport in insulators. Here, using appropriate samples, ultra-low energy Raman spectroscopy a…
Raman spectroscopy plays a key role in studies of graphene and related carbon systems. Graphene is perhaps the most promising material of recent times for many novel applications, including electronics. In this paper, the traditional and well established Kramers-Heisenberg-Dirac (KHD) Raman scattering theory (1925-1927) is extended to crystalline graphene for the first time. It demands different phonon production mechanisms and phonon energies than does the popular "double resonance" Raman scattering model. The latter has never been compared to KHD. Within KHD, phonons are produced instantly a…
Charge density wave (CDW) is a unique phenomenon mostly realized in two-dimensional (2D) metallic layered transition metal dichalcogenides (TMDCs). Here, we report on Raman spectroscopy of single crystal 1T-VSe2 and observed signature of commensurate CDW (C-CDW) and incommensurate (I-CDW) transition, in the temperature range of 50-120 K. The room temperature Raman spectra showed a sharp A1g mode ~ 206 cm-1 along with two new weak and broad Raman modes associated to Eg mode ~ 257 cm-1 and two-phonon mode (2ph) ~ 332 cm-1. The onset of I-CDW and C-CDW is estimated from resistance measurements su…
Isotopic substitution of boron and carbon is applied for the identification of the vibrational modes of heavily boron-doped diamond synthesized by high-pressure high-temperature technique. None of the bands in the Raman spectra are shifting upon ^{10}B-substitution, whereas shifts to lower frequency are observed for all bands upon ^{13}C-substitution as compared to a sample with natural isotope abundancies. These isotopic substitution experiments exclude the hypothesis of boron dimer related normal modes and strongly support the assignment of the previously studied "500 cm^{-1}" and "1230 cm^{…
The Raman selection rules of the (ZnSe, BeSe) mixed phonon polariton created by alloying in the three mode (1ZnSe, 2BeSe) ZnBeSe system, whose dramatic S like dispersion covers the large frequency gap between the ZnSe and BeSe spectral ranges, is studied in its wave vector dependence by near forward scattering. Both the collapse regime away from the Brillouin zone centre and the reinforcement regime near the Brillouin zone centre are addressed, using appropriate laser lines and Be contents. We find that in both regimes the considered phonon polariton, in fact a transverse mode with mixed mecha…
Orhorhombic $α$-MoO$_3$ is a layered oxide with various applications and with excellent potential to be exfoliated as a 2D ultrathin film or monolayer. In this paper, we present a first-principles computational study of its vibrational properties. Our focus is on the zone center modes which can be measured by a combination of infared and Raman spectroscopy. The polarization dependent spectra are simulated. Calculations are also performed for a monolayer form in which "double layers" of Mo$_2$O$_6$ which are weakly van der Waals bonded in the $α$-structure are isolated. Shift in phonon frequenc…
Terahertz-driven parametric excitation of Raman-active phonons in LaAlO$_{3}$
Stockholm University（斯德哥尔摩大学）；Bern University（伯尔尼大学）；CNR-SPIN（意大利国家研究委员会自旋电子学研究所）；Universitá di Salerno（萨莱诺大学）；SLAC National Accelerator Laboratory（斯坦福直线加速器中心）；Temple University（天普大学）；University of California, Berkeley（加州大学伯克利分校）；Department of Molecular Sciences and Nanosystems, Ca’ Foscari University of Venice（威尼斯卡洛·福斯卡里大学分子科学与纳米系统系）
Time-resolved Raman spectroscopy has been applied to probe the anharmonic coupling and electron-phonon interaction of optical phonons in graphite. From the decay of the transient anti-Stokes scattering of the G-mode following ultrafast excitation, we measured a lifetime of 2.2+/-0.1ps for zone-center optical phonons. We also observed a transient stiffening of G-mode phonons, an effect attributed to the reduction of the electron-phonon coupling for high electronic temperatures.
Tailoring phonon-driven responses in α-MoO3 through isotopic enrichment
Vanderbilt University（范德堡大学）；The Pennsylvania State University（宾夕法尼亚州立大学）；Stanford University（斯坦福大学）；University of Virginia（弗吉尼亚大学）；TUD Dresden University of Technology（德累斯顿工业大学）；Istituto Italiano di Tecnologia（意大利理工学院）；Fritz Haber Institute of the Max Planck Society（马克斯·普朗克学会弗里茨·哈伯研究所）；Politecnico di Milano（米兰理工大学）；Helmholtz-Zentrum Dresden-Rossendorf（德累斯顿-罗斯多夫亥姆霍兹中心）；University of Iowa（爱荷华大学）
Raman scattering on phonon--plasmon coupled modes in high magnetic fields is considered theoretically. The calculations of the dielectric function were performed in the long-wave approximation for the semiclassical and ultra-quantum magnetic fields taking into account the electron damping and intrinsic lifetime of optical phonons. The Raman scattering has resonances at the frequencies of coupled modes as well as at multiples of the cyclotron frequency. The dependence of the Raman cross section on the carrier concentration is analyzed.
MnV$_2$O$_4$ in the spinel structure is known to exhibit coupled orbital and spin ordering, and its Raman spectra show interesting anomalies in its low-temperature phase. With a goal to explain this behavior involving coupled spins and phonons, we determine here the spin-phonon couplings in MnV$_2$O$_4$ from a theoretical analysis of its phonon spectra and their dependence on spin-ordering and electron correlations, obtained from first-principles density functional theoretical calculations. Using these in an analysis based on a Landau-like theory, we uncover the mechanism governing the Raman a…
For nanoscale systems such as nanoparticles and 3D-bonded networks, the range of spatial coherence is well reflected in the Raman spectral pattern. For confined, or localized, phonons, the range of q-points contributing to the spectrum depends on the phonon confinement length, which makes possible to derive the size information from the spectra. In this work, Raman spectrum of vitreous silica is described as localized phonons of SiO2 network. The convergence of the spectral pattern with the confinement size is studied. It is shown that the phonon propagation scale in vitreous silica is within …
We consider a model Hamiltonian fitted on the ab-initio band structure to describe the electron-phonon coupling between the electronic $σ-$bands and the phonon E$_{2g}$ mode in MgB$_2$. The model allows for analytical calculations and numerical treatments using very large k-point grids. We calculate the phonon self-energy of the E$_{2g}$ mode along two high symmetry directions in the Brillouin zone. We demonstrate that the contribution of the $σ$ bands to the Raman linewidth of the E$_{2g}$ mode via the electron-phonon coupling is zero. As a consequence the large resonance seen in Raman experi…
The theory of Raman scattering in half-metals by optical phonons interacting with conduction electrons is developed. We evaluate the effect of electron-phonon interactions at ferromagnetic ordering in terms of the Boltzmann equation for carriers. The chemical potential is found to decrease with temperature decreasing. Both the linewidth and frequency shift exhibit a dependence on temperature.
