Long-wavelength Optical Phonons Research Articles

Anisotropic quasi-static permittivity of rare-earth scandate single crystals measured by terahertz spectroscopy

We report the real-valued static and complex-valued quasi-static anisotropic permittivity parameters of rare-earth scandate orthorhombic single crystal GdScO3 (GSO), TbScO3 (TSO), and DyScO3 (DSO). Employing continuous-wave terahertz spectroscopy (0.2–1 THz), the complex permittivity was extracted using an anisotropic ambient-film-ambient model. Data obtained from multiple samples of the same oxides and different surface cuts were analyzed simultaneously. The zero-frequency limit of the modeled data indicates that at room temperature the real part of the dielectric tensor components for GSO are ɛa = 22.7, ɛb = 19.3, and ɛc = 28.1; for DSO, ɛa = 20.3, ɛb = 17.4, and ɛc = 31.1; and for TSO, ɛa = 21.6, ɛb = 18.1, and ɛc = 30.3, with a, b, and c crystallographic axes constituting the principal directions for the permittivity tensor. These results are in excellent agreement with expectations from theoretical computations and with scarcely available data from previous experimental studies. Furthermore, our results evidence a noticeable attenuation, which increases with frequency, and are very significant especially at the higher frequency end of the measurement and along the c-direction in all samples. We suggest the attenuation is most likely caused by the onset of absorption due to long-wavelength active optical phonon modes. These results are important for electronic and potential sub-terahertz applications (e.g., quarter-wave plate) benefiting from the large index contrast along different directions in these materials.

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fr\"ohlich model, which focuses on the nonadiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the $\mathrm{\ensuremath{\Gamma}}$ point. We also incorporate SOC into a generalized Fr\"ohlich model, addressing the Dresselhaus splitting which occurs in noncentrosymmetric materials, and confirm that the predominance of nonadiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fr\"ohlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for noncentrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation, one of the most fundamental assumptions of the Fr\"ohlich model, within the physically relevant energy range of the Fr\"ohlich interaction for materials with high phonon frequencies treated with SOC.

First-principles study of the bandgap renormalization and optical property of β-LiGaO2

The β-LiGaO2 with an orthorhombic wurtzite-derived structure is a candidate ultrawide direct-bandgap semiconductor. In this work, using the non-adiabatic Allen–Heine–Cardona approach, we investigate the bandgap renormalization arising from electron–phonon coupling. We find a sizable zero-point motion correction of –0.362 eV to the gap at Γ, which is dominated by the contributions of long-wavelength longitudinal optical phonons. The bandgap of β-LiGaO2 decreases monotonically with increasing temperature. We investigate the optical spectra by comparing the model Bethe–Salpether equation method with the independent-particle approximation. The calculated optical spectra including electron–hole interactions exhibit strong excitonic effects, in qualitative agreement with the experiment. The contributing interband transitions and the binding energy for the excitonic states are analyzed.

Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement

In polar semiconductors and insulators, the Fr\"ohlich interaction between electrons and long-wavelength longitudinal optical phonons induces a many-body renormalization of the carrier effective masses and the appearence of characteristic phonon sidebands in the spectral function, commonly dubbed 'polaron satellites'. The simplest model that captures these effects is the Fr\"ohlich model, whereby electrons in a parabolic band interact with a dispersionless longitudinal optical phonon. The Fr\"ohlich model has been employed in a number of seminal papers, from early perturbation-theory approaches to modern diagrammatic Monte Carlo calculations. One limitation of this model is that it focuses on undoped systems, thus ignoring carrier screening and Pauli blocking effects that are present in real experiments on doped samples. To overcome this limitation, we here extend the Fr\"ohlich model to the case of doped systems, and we provide exact solutions for the electron spectral function, mass enhancement, and polaron satellites. We perform the analysis using two approaches, namely Dyson's equation with the Fan-Migdal self-energy, and the second-order cumulant expansion. We find that these two approaches provide qualitatively different results. In particular, the Dyson's approach yields better quasiparticle masses and worse satellites, while the cumulant approach provides better satellite structures, at the price of worse quasiparticle masses. Both approaches yield an anomalous enhancement of the electron effective mass at finite doping levels, which in turn leads to a breakdown of the quasiparticle picture in a significant portion of the phase diagram.

Electron-phonon coupling in the magnetic Weyl semimetal ZrCo2Sn

Electron-phonon coupling in $\mathrm{Zr}{\mathrm{Co}}_{2}\mathrm{Sn}$ is investigated within the density-functional theory and linear-response approach in the mixed-basis pseudopotential representation. Phonon-induced scattering is analyzed for excited electrons (holes) in two majority bands, which form the topological Weyl state. Although the electron-phonon coupling in the energy range under consideration demonstrates some dependence on the available phase space, the strength of the phonon-mediated scattering, $\ensuremath{\lambda}$, changes rather weakly with the hole (electron) energy and momentum, varying between 0.1 and 0.3. The momentum-averaged value of $\ensuremath{\lambda}$ ranges from 0.25 to 0.45. The phonon-mediated scattering of electrons near the Weyl point is found to be weak enough to warrant well-defined quasiparticles. Most of the modes actively involved in electron scattering are middle- and high-frequency lattice vibrations, while the participation of low-energy acoustic phonons is significantly suppressed by electron-phonon matrix elements. Of the long-wavelength optical phonons, only the ${T}_{2g}$ Raman active modes generated by opposite vibrations of Co atoms make a noticeable contribution to the scattering of electrons.

Electron-phonon interaction and zero-field charge carrier transport in the nodal-line semimetal ZrSiS

We study electron-phonon interaction and related transport properties of nodal-line semimetal ZrSiS using first-principles calculations. We find that ZrSiS is characterized by a weak electron-phonon coupling on the order of 0.1, which is almost energy independent. The main contribution to the electron-phonon coupling originates from long-wavelength optical phonons, causing no significant renormalization of the electron spectral function. At the charge neutrality point, we find that electrons and holes provide a comparable contribution to the scattering rate. The phonon-limited resistivity calculated within the Boltzmann transport theory is found to be strongly direction-dependent with the ratio between out-of-plane and in-plane directions being $\rho_{zz}/\rho_{xx}\sim 7.5$, mainly determined by the anisotropy of carrier velocities. We estimate zero-field resistivity to be $\rho_{xx}\approx12$ $\mu\Omega$ cm at 300 K, which is in good agreement with experimental data. Relatively small resistivity in ZrSiS can be attributed to a combination of weak electron-phonon coupling and high carrier velocities.

Emergence of large nonadiabatic effects induced by the electron-phonon interaction on the complex vibrational quasiparticle spectrum of doped monolayer MoS2

We present a comprehensive first-principles analysis of the nonadiabatic effects due to the electron-phonon interaction on the vibrational spectrum of the electron-doped monolayer ${\mathrm{MoS}}_{2}$. Deep changes in the Fermi surface upon doping cause the linewidth broadening of the normal modes governing the spin-conserving intervalley electronic scattering, which become unstable with the population of all the spin-split conduction valleys. We find that the nonadiabatic spectral effects modify dramatically the adiabatic dispersion of the long-wavelength optical phonon modes, responsible for intravalley scattering, as soon as inequivalent valleys get populated. These results are illustrated by means of a simple analytical model. Finally, we explain the emergence of an intricate dynamical structure for the strongly interacting out-of-plane polarized ${A}_{1}^{\ensuremath{'}}$ optical vibrational mode spectrum by means of a multiple-phonon quasiparticle picture defined in the full complex frequency plane, showing that this intriguing spectral structure originates from the splitting of the original adiabatic branch induced by the electron-phonon coupling.

Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids.

We present a microscopic picture rationalizing the surprisingly steep decrease in the bandgap with temperature in insulators, crystalline or otherwise. The gap narrowing largely results from fluctuations of long-wavelength optical phonons-when the latter are present-or their disordered analogs if the material is amorphous. We elaborate on this notion to show that possibly with the exception of weakly bound solids made of closed-shell electronic configurations, the existence of an insulating gap or pseudogap in a periodic solid implies that optical phonons must be present, too. This means that in an insulating solid, the primitive cell must have at least two atoms and/or that a charge density wave is present, with the possible exception of weakly bonded solids such as rare-gas or ferromagnetic Wigner crystals. As a corollary, a (periodic) elemental solid held together by nonclosed shell interactions and whose primitive unit contains only one atom will ordinarily be a metal, consistent with observation. Consequences of the present picture for Wigner solids are discussed. A simple field theory of the metal-insulator transition is constructed that directly ties long-wavelength optical vibrations with fluctuations of an order parameter for the metal-insulator transition. The order parameter is shown to have at least two components, yet no Goldstone mode arises as a result of the transition.

Splitting of frequencies of optical phonons in tensile-strained germanium layers

Tensile-strained germanium films in Ge/GeSn/Si/GeSnSi multilayer heterostructures grown by molecularbeam epitaxy on Si(001) substrates are investigated by Raman spectroscopy. Biaxial tensile strains in the films reach 1.5%, which exceeds values previously obtained for this system. Splitting of frequencies of long-wavelength optical phonons is experimentally observed; i.e., the shift of the frequency of the singlet induced by biaxial tensile strains is larger than the shift of the frequency of the doublet in agreement with calculations. The strain-induced shift of Raman scattering peaks from two-phonon scattering in germanium is also detected.

Optical properties of lithium gallium oxide

The optical dielectric function tensor of orthorhombic single-crystal LiGaO2 was determined for polarizations along a, b, and c crystal-axis in the photon energy range from 0.04eV to 6.5eV by the generalized spectroscopic ellipsometry. In the far-infrared spectral range from 12.4meV to 40meV, the dielectric function was determined from conventional polarized transmittance and polarized reflectance measurements. Lineshape analysis of the dielectric function tensor major components allowed for a determination of the long-wavelength optical phonon characteristics, refractive indices dispersion, and parameters of interband and excitonic optical transitions.

Angular dependence of Raman scattering selection rules for long-wavelength optical phonons in short-period GaAs/AlAs superlattices

The angular dependence of Raman scattering selection rules for optical phonons in short-period (001) GaAs/AlAs superlattices is calculated and experimentally studied. Experiments are performed using a micro-Raman setup, in the scattering geometry with the wavevectors of the incident and scattered light lying in the plane of superlattices (so-called in-plane geometry). Phonon frequencies are calculated using the Born model taking the Coulomb interaction into account in the rigid-ion approximation. Raman scattering spectra are calculated in the framework of the deformation potential and electro-optical mechanisms. Calculations show an angular dependence of the selection rules for optical phonons with different directions of the wavevectors. Drastic differences in the selection rules are found for experimental and calculated spectra. Presumably, these differences are due to the Frohlich mechanism in Raman scattering for short-period superlattices.

Long-wavelength optical phonon behavior in uniaxial strained graphene: Role of electron-phonon interaction

We derive the frequency shifts and the broadening of $\ensuremath{\Gamma}$-point longitudinal optical (LO) and transverse optical (TO) phonon modes, due to electron-phonon interaction, in graphene under uniaxial strain as a function of the electron density and the disorder amount. We show that, in the absence of a shear strain component, such interaction gives rise to a lifting of the degeneracy of the LO and TO modes which contributes to the splitting of the G Raman band. The anisotropy of the electronic spectrum, induced by the strain, results in a polarization dependence of the LO and TO modes. This dependence is in agreement with the experimental results showing a periodic modulation of the Raman intensity of the split G peak. Moreover, the anomalous behavior of the frequency shift reported in undeformed graphene is found to be robust under strain.

Anisotropy of long-wavelength optical phonons in GaAs/AlAs superlattices

The angular anisotropy of optical phonons in GaAs/AlAs (001) superlattices is investigated by Raman scattering spectroscopy. Scattering configurations allowed for phonons with wave vectors oriented along the superlattice layers and normally to them are used. For phonons localized in GaAs layers, the theoretically predicted mixing of the LO1 longitudinal modes with TO1 transverse modes in which atomic displacements occur along the normal to the superlattice is observed experimentally. These modes possess noticeable angular anisotropy. For transverse modes in which atoms move in the plane of the superlattice, the angular anisotropy is small.

Generalized Pseudo-Unit-Cell model for long-wavelength optical phonons of multinary mixed crystals: Application to AxB_1−xCyD_1−y type mixed crystals

Long-wavelength optical phonons in multinary mixed crystals are studied based on the Pseudo-Unit-Cell model. A unitary matrix method is developed to calculate the eigenfrequencies of optical phonons in multinary mixed crystals. The analytical expressions of oscillator strengths and dielectric constants of the multinary mixed crystals are obtained as a function of the phonon frequencies. The results indicate that the composition dependence of oscillator strengths shows clearly the phonon-mode behaviors of the mixed crystals. The theory and calculation method can be applied to any type of multinary mixed crystals. It is found that there is a composition independent point for the dielectric constant of quaternary mixed crystals.

Long-wavelength optical phonons in mixed crystal AB1 − x C x

The properties of long-wavelength optical phonons in mixed crystals are discussed within the framework of a model similar to modified random-element-isodisplacement (MREI) model. This model can be applied to the one-mode behavior, the two-mode behavior and that of the third category. The frequency and the electron-phonon coupling constants varying with the concentration ratio x is obtained.

Optical Spectrum Analyses of ZnS<sub>1-X</sub>Se<sub>x</sub> Ternary Material

The lattices motion equation and Born-Huang equation was established with the framework of modified random-element-isodisplacement (MREI) model, and the relationship of dielectric constants of lattice vibration and FT-IR reflectivity spectra in ternary mixed crystals ZnS1-xSex with the changes of composition x are discussed. The two-mode behavior of long-wave length optical phonon was studied, and the relation of TO-phonon frequency and LO-phonon frequency with composition was obtained.

Contribution of long-wavelength transverse optical phonons to electron–phonon coupling in doped polar insulators

We estimate the contribution of the long-wavelength el–TO–ph interaction and discuss the effect it has on electron–phonon scatterings in doped polar systems like SrTiO 3 and PbTe. The analytical and numerical results presented in the study indicate that the el–TO–ph interaction tends to contribute little to the total strength of electron–phonon coupling in these and related materials. To explain this fact we consider possible reasons why the effect of the polar long-wavelength transverse optical phonons on the coupling constant λ is far less than one might suppose.

The lifetime of optical phonons in a single heterostructure

The lifetime of long-wavelength optical phonons in bulk semiconductors is known to be a function of electron density, decreasing with increasing density. An explanation of this has been given in terms of the effect of plasmon coupling on the anharmonic decay route. This explanation is limited to small wave vectors and is not applicable to the case of phonons in general because their interaction with electrons involves larger wave vectors for which the plasma coupling is Landau damped. Nevertheless, a similar decrease of lifetime with density is observed for hot phonons in the channel of a GaN Heterostructure Field Effect Transistor (HFET). We show that this dependence on electron density can be associated with the interaction with the barrier interface mode and the temperature dependence of the phonon lifetimes. It is pointed out that a complete account of the shortening of phonon lifetime in a working HFET requires an analysis of the specific thermal and electron transport properties of thesystem. Important differences arise between HFETs grown on sapphire and on SiC.

Hot phonons in a single heterostructure

The lifetime of long-wavelength optical phonons in bulk semiconductors is known to be a function of electron density, decreasing with increasing density. An explanation of this has been given in terms of the effect of plasmon coupling on the anharmonic decay route. This explanation is limited to small wave-vectors and is not applicable to the case of phonons in general, since their interaction with electrons involves larger wave-vectors for which the plasma coupling is Landau damped. Nevertheless, a similar decrease of lifetime with density is observed for hot phonons in the channel of a GaN HFET. We offer an explanation of this in terms of a lifetime of interface modes significantly shorter than that of bulk modes. Our explanation also applies qualitatively to the observation of the non-monotonic behaviour of phonon lifetime with electron density.

Multiple-peak structure in porous Si photoluminescence

Photoluminescence (PL) measurements have been carried out on anodic porous silicon (PSi) at temperatures between T=20 and 300 K. He–Ne laser (1.96 eV), green laser diode (2.33 eV), and He–Cd laser (3.81 eV) are used as excitation light sources. Low-temperature (T≤250 K) PL spectra show a multiple-peak structure even when laser excitation is far from resonance with the red PL band. The configurational-coordinate model explains such unique multiple-peak structure very well. Fourier transform (FT) technique is used for the analysis of the measured multiple-peak structure. The FT frequency is determined to be ∼64 meV, which is in exact agreement with the bulk long-wavelength optical phonon energy in crystalline Si. Although the origin of the multiple-peak structure is bulk-related, its strength is very sensitive to the presence of surface oxide.