Longitudinal Acoustic Phonon Branches Research Articles

Chemical doping induced zone-edge phonon renormalization in single-layer MoS2

Chemical doping is an effective method for tailoring physical properties of semiconductors. It has been long known that trace-level doping can obviously influence vibrational properties of bulk semiconductors. Nevertheless, less is known about the effect of chemical doping on the lattice dynamics of two-dimensional (2D) semiconductors although electron-phonon interaction can significantly influence the electronic mobility of the 2D semiconductors. In this study, we carried out Raman-scattering measurements in combine with atom-resolved scanning transmission electron microscope characterization to unveil the effects of Re doping on the phonon dispersion of single-layer (1L) $\mathrm{Mo}{\mathrm{S}}_{2}$. Second-order Raman modes in a wide spectral range reveal the distinct softening of the longitudinal acoustic phonon branch of 1L $\mathrm{Mo}{\mathrm{S}}_{2}$ but with an imperceptible shift of other branches. Such zone-edge phonon renormalization mainly results from electron doping via strong electron-phonon coupling along with a minor contribution from the increased atomic weight from heavier Re dopants. This study enriches the understanding of dopant-host interactions in 2D materials in the aspect of phonons, which is important for tailoring physical properties of 2D materials, such as thermal and electrical transport.

Thermal conduction in single-layer black phosphorus: highly anisotropic?

The single-layer black phosphorus is characteristic for its puckered structure, which has led to distinct anisotropy in its optical, electronic, and mechanical properties. We use the non-equilibrium Greenʼs function approach and the first-principles method to investigate the thermal conductance for single-layer black phosphorus in the ballistic transport regime, in which the phonon–phonon scattering is neglected. We find that the anisotropy in the thermal conduction is very weak for the single-layer black phosphorus—the difference between two in-plane directions is less than 4%. Our phonon calculations disclose that the out-of-plane acoustic phonon branch has lower group velocities in the direction perpendicular to the pucker, as the black phosphorus is softer in this direction, leading to a weakening effect for the thermal conductance in the perpendicular direction. However, the longitudinal acoustic phonon branch behaves abnormally; i.e., the group velocity of this phonon branch is higher in the perpendicular direction, although the single-layer black phosphorus is softer in this direction. The abnormal behavior of the longitudinal acoustic phonon branch is closely related to the highly anisotropic Poissonʼs ratio in the single-layer black phosphorus. As a result of the counteraction between the out-of-plane phonon mode and the in-plane phonon modes, the thermal conductance in the perpendicular direction is weaker than the parallel direction, but the anisotropy is pretty small.

Layer‐dependent resonant Raman scattering of a few layer MoS2

We report resonant Raman scattering of MoS2 layers comprising of single, bi, four and seven layers, showing a strong dependence on the layer thickness. Indirect band gap MoS2 in bulk becomes a direct band gap semiconductor in the monolayer form. New Raman modes are seen in the spectra of single‐ and few‐layer MoS2 samples which are absent in the bulk. The Raman mode at ~230 cm−1 appears for two, four and seven layers. This mode has been attributed to the longitudinal acoustic phonon branch at the M point (LA(M)) of the Brillouin zone. The mode at ~179 cm−1 shows asymmetric character for a few‐layer sample. The asymmetry is explained by the dispersion of the LA(M) branch along the Γ‐M direction. The most intense spectral region near 455 cm−1 shows a layer‐dependent variation of peak positions and relative intensities. The high energy region between 510 and 645 cm−1 is marked by the appearance of prominent new Raman bands, varying in intensity with layer numbers. Resonant Raman spectroscopy thus serves as a promising non invasive technique to accurately estimate the thickness of MoS2 layers down to a few atoms thick. Copyright © 2012 John Wiley & Sons, Ltd.

Structural, dynamical and thermodynamics properties of YBi

We have performed first-principles calculations using the full-potential linear augmented plane-wave, plane wave pseudopotential methods and density linear-response theory to study the structural, electronic, dynamical and thermodynamic properties of the yttrium bismuth YBi. Total energy calculations of the zinc-blende, rocksalt, and cesium chloride phases are investigated. The NaCl structure is found to be the ground state phase of YBi. Bismuth atom induces strong relativistic effects, creating a large spin–orbit splitting of ∼2000meV. Moreover, the phonon band structure is characterized by an appreciable overlap between longitudinal and transverse optical modes. Furthermore we found that the transverse and longitudinal acoustic phonon branches show respectively small variation along the X→W and W→L directions, while the longitudinal optical modes show flatness along a large part of the Brillouin zone. Bismuth atoms show low vibrational amplitudes as compared with yttrium atoms. Moreover we found a strong contribution to heat capacity and entropy from optical (acoustic)-modes of Y (Bi) atoms, with relatively small contribution of Y-acoustic modes and a vanishing contribution of optical modes of Bi.

Theory of surface phonons at metal surfaces: recent advances

Recent studies of the surface dynamics of Al(001) and Cu(111) based on densityfunctional perturbation theory have substantiated the existence of subsurface opticalphonon resonances of all three polarizations, thus confirming early predictionsof the embedded-atom method. The hybridization of the shear-vertical opticalresonance with the longitudinal acoustic phonon branch accounts for the ubiquitousanomalous acoustic resonance as an intrinsic feature of metal surfaces. The DFPTcalculation of the phonon-induced surface charge density oscillations shows that heliumatom scattering spectroscopy (HAS) can indeed probe subsurface resonances.This opens new perspectives to HAS for the measurement of subsurface phonondispersion curves in thin films, as proved by recent HAS studies on Pb and Feultrathin films on copper. After discussing these recent advances, this paper brieflyreviews other important trends of surface dynamics expressed in recent years.

Phonon density of states of SmS under high pressure determined byS149mnuclear inelastic scattering

The impact of the pressure-induced valence transition on the phonon density of states (DOS) in SmS was studied by $^{149}\text{S}\text{m}$ nuclear inelastic scattering of synchrotron radiation. The derived phonon DOS shows drastic differences between the divalent phase at ambient pressure and the intermediate valent phase at 1.5, 2.9, and 4.6 GPa. The phonon DOS at ambient pressure shows two peaks which can be assigned to the transverse-acoustic (TA) and longitudinal-acoustic (LA) phonon branches, while at high pressures only one broad peak is observed. The data were analyzed with a simple model for the TA and LA phonon branches, which could well describe the measured spectra. In the intermediate valent phase the pressure dependence of the cutoff energies of the TA and LA phonon branches is very different and reflects the strong modifications of the LA branches in the intermediate valent phase. This behavior is also responsible for a characteristic variation in the derived Lamb-M\ossbauer factors and Debye temperatures.

Excitation of the shear horizontal mode in a monolayer by inelastic helium atom scattering

Inelastic scattering of a low-energy atomic helium beam (HAS) by a physisorbed monolayer is treated in the one-phonon approximation using a time-dependent wave packet formulation. The calculations show that modes with shear horizontal polarization can be excited near high symmetry azimuths of the monolayer, in agreement with recent experiments. The parameters of the calculations are chosen to match the conditions of HAS experiments for triangular incommensurate monolayer solids of xenon, krypton, and argon adsorbed on the (111) face of platinum, and the results show many of the systematic experimental trends for relative excitation probability of the shear horizontal and longitudinal acoustic phonon branches. The inelastic scattering at beam energies near 8 meV is exceedingly sensitive to small misalignment between the scattering plane and the high symmetry directions of the monolayer solid. The diffraction and inelastic processes arise from a strong coupling of the incident atom to the target and the calculated results show large departures from expectations based on analogies to inelastic thermal neutron scattering.

Polarization properties, high-order Raman spectra, and frequency asymmetry between Stokes and anti-Stokes scattering of Raman modes in a graphite whisker

The Raman spectra of a new type of graphite whiskers have been measured in the range of $150--7800{\mathrm{cm}}^{\ensuremath{-}1}.$ The intensity of the overtone $(2D)$ located at $\ensuremath{\sim}2700{\mathrm{cm}}^{\ensuremath{-}1}$ is found to be about 10 times stronger than that of the C-C stretching mode (G) at $1582{\mathrm{cm}}^{\ensuremath{-}1}.$ Because of the peculiar enhancement of the $2D$ mode, high-order Raman bands up to fifth order at $\ensuremath{\sim}7500{\mathrm{cm}}^{\ensuremath{-}1}$ have been observed. Polarized micro-Raman spectroscopy has been performed on an individual graphite whisker, and angular-dependent intensity measurements of all Raman modes in the $\mathrm{VV}$ and $\mathrm{HV}$ geometries are in agreement with the theoretical calculated results. Laser-energy-dependent dispersion effects and the frequency discrepancy of Raman modes between their Stokes and anti-Stokes lines in graphite whiskers are also carefully investigated. The energy dispersion of the D mode and G mode is very similar to that of highly oriented pyrolytic graphite (HOPG). In contrast to the Raman spectra of HOPG and other graphite materials, two laser-energy-dependent Raman lines are revealed in the low-frequency region of the Raman spectra of graphite whiskers, which are believed to be the resonantly enhanced phonons in the transverse-acoustic and longitudinal-acoustic phonon branches. Moreover, the obvious energy dispersion of the ${D}^{\ensuremath{'}}$ mode at \ensuremath{\sim}1620 ${\mathrm{cm}}^{\ensuremath{-}1}$ is observed in graphite whiskers. The results clearly reveal how strongly the peak parameters of Raman modes of graphite materials are dependent on their structural geometry. The Stokes and anti-Stokes scattering experiments show that the frequency discrepancy between the Stokes and anti-Stokes sides of a Raman mode in graphite materials is equal to the frequency value covered by the one-phonon energy of this Raman mode in its frequency versus laser energy curve, which is the product of the one-phonon energy of this mode $(E{\ensuremath{\omega}}_{s})$ and the value of its laser-energy dispersions $(\ensuremath{\partial}E{\ensuremath{\omega}}_{s}/\ensuremath{\partial}{\ensuremath{\varepsilon}}_{L}).$

Dispersion relations of acoustic phonons in pyrope garnet; relationship between vibrational properties and elastic constants

Coherent inelastic neutron scattering measurements have been performed on a natural garnet pyrope from the Dora Maira Massif, Italian Western Alps, [(M&.92Feo.osCao.o3)3Al2Si3012, space group Ia'Jd, Z = 8, a = 11.459 A] to determine the acoustic phonon-dispersion relations at room temperature. Phonon measurements have not previously been made on natural garnets, although the dispersion curves form a basis for developing and testing physically correct interatomic potentials for use in lattice dynamical models. Acoustic phononspropagating in the high-symmetry [100]and [110]directions were observed using the PRISMA spectrometer installed at the ISIS Neutron Spallation Source, U.K. The inelastic scans were performed around the (660), (080), (860), (10,6,0), and (0,10,0) Bragg points: Two transverse acoustic and one longitudinal acoustic phonon branches were measured. The observed acoustic phonon frequencies are in good agreement with those calculated on the basis of a semiempirical interatomic potential model. As a check, the elastic constants obtained from the slopes of the acoustic phonon branches are comparable with previous measurements obtained by Brillouin spectroscopy, although their large estimated errors reflectthe complexityof the experimentalmeasurements of phonon-dispersion curves on pyrope garnets.

Optical properties of molecular conductors: One-dimensional systems with twofold-commensurate charge-density waves.

A model is presented for the optical properties in the near to far infrared of a twofold-commensurate one-dimensional system of noninteracting molecular-ion chains. Each chain may be subject to an arbitrary type of lattice distortion that doubles the periodicity of the regular chain and is composed of a lattice dimerization (LD) and/or an alternating molecular deformation (AMD). The effect of an external potential induced by the presence of nearby chains of closed-shell counterions is also accounted for. The linear coupling of the electrons to an arbitrary number of intramolecular modes and to one longitudinal acoustic phonon branch is treated in the adiabatic linear-response approximation. No direct electron-electron interaction is explicitly included but the limit case of noninteracting spinless fermions in a large-U system can be dealt with in the present scheme. The results of the model can be directly applied to the analysis of the experimental infrared data of many conducting organic radical salts of 2:1 stoichiometry where LD and/or AMD of small amplitude occur and the on-site electron-electron correlation is thought to play a major role. The model fitting of the data can be used to obtain information on the one-electron bandwidth, the individual contributions to the total gap of charge density waves components centered on the bonds and on the sites, the relevance of the counterion potential, and the strength of the electron-phonon and electron-molecular vibration interactions. Some of these potentialities as well as the ``selection rules'' governing the infrared activity of the intramolecular and intermolecular modes as phase phonons are illustrated by numerical model calculations. Self-consistent relations and practical criteria that allow one to use the minimal number of adjustable parameters in the calculations are also presented.

Lattice dynamics of mixed-valent SmS

Neutron scattering techniques have been used to measure the phonon dispersion curves for SmS in both the semiconducting and the metallic mixed-valent state. Large softening of the longitudinal acoustic phonon branches was found in the mixed-valent state, particularly for the [111] direction. It is apparent there is a strong coupling between the valence fluctuations and the phonons in the mixed-valent phase of SmS.

Magnons and Phonons in Cobalt Ferrite

Magnons and phonons have been observed in a single crystal of cobalt ferrite, CoFe2O1 at room temperature. Dispersion relations are plotted for the [001] and the [111] directions. The longitudinal acoustic phonon branch has been measured out to the zone boundary in both directions, while the transverse acoustic branch has been completely determined only in the [001] direction. The acoustic magnon branches are well defined at low energies, but they rapidly lose intensity and disappear at around 9 THz. We have not determined uniquely why this happens, but some possibilities are given. Optic branches have been observed at around 11.3 and 14.0 THz. Infrared data indicate that the first branch is probably of phonon character and the second of magnon character.