Transition metal dichalcogenides like MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$ have attracted enormous interest during recent years. They are van-der-Waals crystals with highly anisotropic properties, which allows exfoliation of individual layers. Their remarkable physical properties make them promising for applications in optoelectronic, spintronic, and valleytronic devices. Phonons are fundamental to many of the underlying physical processes, like carrier and spin relaxation or exciton dynamics. However, experimental data of the complete phonon dispersion relations in these materials is missing. Here we present the phonon dispersion of bulk MoS$_2$ in the high-symmetry directions of the Brillouin zone, determined by inelastic X-ray scattering. Our results underline the two-dimensional nature of MoS$_2$. Supported by first-principles calculations, we determine the phonon displacement patterns, symmetry properties, and scattering intensities. The results will be the basis for future experimental and theoretical work regarding electron-phonon interactions, intervalley scattering, as well as phonons in related 2D materials.
The thermal conductivity $κ$ of a material is an important parameter in many different applications. Optimization strategies of $κ$ often require insight into the dominant phonon scattering processes of the material under study. The Callaway model is widely used as an experimentalist's tool to analyze the lattice part of the thermal conductivity, $κ_l$. Here, we investigate how deviations from the implicitly assumed linear phonon dispersion relation affect $κ_l$ and in turn conclusions regarding the relevant phonon scattering processes. As an example, we show for the half-Heusler system (Hf,Zr…
Using Landau-Ginsburg-Devonshire theory, we derive and analyze analytical expressions for the frequency dispersion of soft phonon modes in nanosized ferroics and perform numerical calculations for a thin SrTiO3 film. We revealed the pronounced "true" size effect in the dependence of soft phonon spatial dispersion on the film thickness and predict that it can lead to the "apparent" or "false" size effect of dynamic flexoelectric coupling constants
We here introduce a Fortran code that computes anharmonic free energy of solids from first-principles based on our phonon quasiparticle approach. In this code, phonon quasiparticle properties, i.e., renormalized phonon frequencies and lifetimes, are extracted from mode-projected velocity auto-correlation functions (VAF) of modes sampled by molecular dynamics (MD) trajectories. Using renormalized frequencies as input, the code next constructs an effective harmonic force constant matrix to calculate anharmonic phonon dispersions over the whole Brillouin zone and thus the anharmonic free energy i…
Microscopic coupling between the electron spin and the lattice vibration is responsible for an array of exotic properties from morphic effects in simple magnets to magnetodielectric coupling in multiferroic spinels and hematites. Traditionally, a single spin-phonon coupling constant is used to characterize how effectively the lattice can affect the spin, but it is hardly enough to capture novel electromagnetic behaviors to the full extent. Here, we introduce a concept of spin-phonon dispersion to project the spin moment change along the phonon crystal momentum direction, so the entire spin cha…
We have measured the room-temperature phonon spectrum of Mo-stabilized $γ-$U. The dispersion curves show unusual softening near the H point, q=[1/2,1/2,1/2], which may derive from the metastability of the $γ-$U phase or from strong electron-phonon coupling. Near the zone center, the dispersion curves agree well with theory, though significant differences are observed away from the zone center. The experimental phonon density of states is shifted to higher energy compared to theory and high-temperature neutron scattering. The elastic constants of $γ$-UMo are similar to those of body-centered cu…
The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized near the interface. These interface phonons play an essential role in thermal/electrical transport properties in devices especially in miniature ones wherein the interface may dominate the entire response of the device. Knowledge of phonon dispersion at interfaces is therefore highly desirable for device design and optimization. Although theoretical work has begun decades ago, experimental research is totally absent due to challenges in achieving combined spatial, momentum and spect…
A recent inelastic x-ray scattering study [Manley et al., Phys. Rev. B 85, 132301 (2012)] reveals that the phonon dispersion curves of PuO2 is considerably consistent with our previous density functional +$U$ results [Zhang et al., Phys. Rev. B 82, 144110 (2010)]. Here in the present work, using the same computational methods, we further obtain the phonon dispersion curves for α-Pu2O3. We find that the Pu-O bonding is weaker in α-Pu2O3 than in fluorite PuO2, and subsequently a frequency gap appears between the vibrations of oxygen and plutonium atoms. Based on the phonon dispersion curves and …
We present Phonon Unfolding, a Fortran90 program for unfolding phonon dispersions. It unfolds phonon dispersions by using a generalized projection algorithm, which can be used to any kind of atomic systems in principle. Thus our present program provides a very useful tool for the phonon dispersion and vibration mode analysis of surface reconstructions, atomic point defects, alloys and glasses.
We calculate the phonon spectrum for a graphene sheet resulting from the model proposed by T. Lenosky et al. (Nature 355, 333 (1992)) for the free energy of the lattice. This model takes into account not only the usual bond bending and stretching terms, but captures the possible misalignment of the pz orbitals. We compare our results with previous models used in the literature and with available experimental data. We show that while this model provides an excellent description of the flexural modes in graphene, an extra term in the energy is needed for it to be able to reproduce the full phono…
The orthovanadates are useful as host matrices for immobilization of radioactive wastes. The thermodynamic stability of these materials is crucial for their applications in high pressure and temperatures environment. It is necessary to investigate the phonons in the entire Brillouin zone, beyond the zone-centre phonons accessible in previous Raman and infrared experiments. We have carried out extensive neutron inelastic scattering experiments to derive the phonon dispersion relation of YVO4 up to high energy transfer of 65 meV using a single crystal, which are perhaps reported for the first ti…
The lattice dynamics of AgPd, Ni55Pd45, Ni95Pt05, and Cu0.715Pd0.285 intermetallic have been investigated using the DFT calculation. The phonon dispersions and phonon densities of states along for two symmetry directions are calculated by Weighted Dynamical Matrix (WDM) and compared with virtual crystal approximation (VCA), supercell approach, and inelastic neutron scattering experimental results. The impact of mass, force-constant fluctuation, and Ag concentration on lattice dynamics of AgPd are discussed, and a comparison between WDM and Supercell approach is performed. The averaged first Ne…
We have studied the electronic, magnetic and linear phonon dispersion behavior of Phosphorene monolayer using rst principle based ab initio method. Phosphorene monolayer is a semiconducting system with a dimensional dependent variable range of band gap. Vacancy has been done to study the geometry and physical behavior of the monolayer system. Pristine, vacancy induced monolayer and vacancy induced doped monolayer are included in the calculation. Dopant concentration has been well checked via optimization algorithm to maintain the dilute magnetic semiconducting behavior of the monolayer system.…
We report first-principles calculations of the phonon dispersion spectrum, thermal expansion, and heat capacity of uranium dioxide. The so-called direct method, based on the quasiharmonic approximation, is used to calculate the phonon frequencies within a density functional framework for the electronic structure. The phonon dispersions calculated at the theoretical equilibrium volume agree well with experimental dispersions. The computed phonon density of states (DOS) compare reasonably well with measurement data, as do also the calculated frequencies of the Raman and infrared active modes inc…
We introduce a class of two-dimensional non-resonant single-phase phononic materials and investigate its peculiar dispersion characteristics. The material consists of a thin plate-like structure with an embedded periodic lattice of Acoustic Black Holes. The use of these periodic tapers allows achieving remarkable dispersion properties such as Zero Group Velocity in the fundamental modes, negative group refraction index, bi-refraction, and mode anisotropy. The dispersion properties are numerically investigated using a three-dimensional supercell plane wave expansion method. The effect on the di…
We present first principles calculations of the phonon dispersions of Bi2Te3 and discuss these in relation to the acoustic phonon interface scattering in ceramics. The phonon dispersions show agreement with what is known from neutron scattering for the optic modes. We find a difference between the generalized gradient approximation and local density results for the acoustic branches. This is a consequence of an artificial compression of the van der Waals bonded gaps in the Bi2Te3 structure when using the generalized gradient approximation. As a result local density approximation calculations p…
We calculate the phonon-dispersion relations of several two-dimensional materials and diamond using the density-functional based tight-binding approach (DFTB). Our goal is to verify if this numerically efficient method provides sufficiently accurate phonon frequencies and group velocities to compute reliable thermoelectric properties. To this end, the results are compared to available DFT results and experimental data. To quantify the accuracy for a given band, a descriptor is introduced that summarizes contributions to the lattice conductivity that are available already in the harmonic approx…
Using a full dispersion description of phonons, the thermal conductivities of bulk Si and Bi2Te3 are evaluated using a Landauer approach and related to the conventional approach based on the Boltzmann transport equation. A procedure to extract a well-defined average phonon mean-free-path from the measured thermal conductivity and given phonon-dispersion is presented. The extracted mean-free-path has strong physical significance and differs greatly from simple estimates. The use of simplified dispersion models for phonons is discussed, and it is shown that two different Debye temperatures must …
The thermal conductivity of boron arsenide (BAs) is believed to be influenced by phonon scattering selection rules due to its special phonon dispersion. Compression of BAs leads to significant changes in phonon dispersion, which allows for a test of first principles theories for how phonon dispersion affects three- and four-phonon scattering rates. This study reports the thermal conductivity of BAs from 0 to 30 GPa. Thermal conductivity vs. pressure of BAs is measured by time-domain thermoreflectance with a diamond anvil cell. In stark contrast to what is typical for nonmetallic crystals, BAs …
An approach to compute the anharmonic peaks of the phonon dispersion curves through the ab initio calculated Hellmann-Feynman forces from a series of supercells with realistic atomic displacements of all atoms, which correspond to a given temperature, is reported. Obtained phonon dispersion bands are able to represent the positions and shapes of the anharmonic peaks. As example, the approach to cubic PbTe and perovskite MgSiO3 crystals is applied.
It is well known that conventional harmonic lattice dynamics cannot be applied to energetically unstable crystals at 0 K, such as high temperature body centered cubic (BCC) phase of crystalline Zr. Predicting phonon spectra at finite temperature requires the calculation of force constants to the third, fourth and even higher orders, however, it remains challenging to determine to which order the Taylor expansion of the potential energy surface for different materials should be cut off. Molecular dynamics, on the other hand, intrinsically includes arbitrary orders of phonon anharmonicity, howev…
We present ab-initio phonon dispersion relations for the three lead chalcogenides PbS, PbSe, and PbTe. The acoustic branches are in very good agreement with inelastic neutron-scattering data and calculations of the specific heat give good agreement with experimental data. The pronounced minimum of the transverse optical branch at Gamma due to the near-ferroelectricity of the lead chalcogenides is qualitatively reproduced. In addition, we find a pronounced dip in the longitudinal optical branch at Gamma. This dip was previously explained as the effect of "free carriers" (due to the presence of …
Direct measurement of local phonon dispersion in individual nanostructures can greatly advance our understanding of their electrical, thermal, and mechanical properties. However, such experimental measurements require extremely high detection sensitivity and combined spatial, energy and momentum resolutions, thus has been elusive. Here, we develop a four-dimensional electron energy loss spectroscopy (4D-EELS) technique based a monochromated scanning transmission electron microscope (STEM), and present the position-dependent phonon dispersion measurement in individual boron nitride nanotubes (B…
An increasing number of theoretical calculations on few-layer materials have been reporting a non-zero sound velocity for all three acoustic phonon modes. In contrast with these reports, here we show that the lowest phonon dispersion branch of atomistically described few-layer materials should be quadratic, and this can have dramatic consequencies on calculated properties, such as the thermal conductivity. By reformulating the interatomic force constants (IFC) in terms of internal coordinates, we find that a delicate balance between the IFCs is responsible for this quadraticity. This balance i…
The phonon dispersion unfolding method is useful for obtaining hidden Bloch symmetries and comparing theoretical results with experiment spectrums (e.g., inelastic neutron scattering, inelastic X-ray scattering, Raman). In this paper, we propose a method to unfold phonon dispersions. The main advantage of this method is the ability to handle systems with heavy breaking of spatial translational symmetry. Its validity is tested by pure diamond, diamond with Si substitution, and diamond with C vacancies.
Phonon dispersions in <100> silicon nanowires (SiNW) are modeled using a Modified Valence Force Field (MVFF) method based on atomistic force constants. The model replicates the bulk Si phonon dispersion very well. In SiNWs, apart from four acoustic like branches, a lot of flat branches appear indicating strong phonon confinement in these nanowires and strongly affecting their lattice properties. The sound velocity (Vsnd) and the lattice thermal conductance (kl) decrease as the wire cross-section size is reduced whereas the specific heat (Cv) increases due to increased phonon confinement and su…
Computational study of structural, elastic, electronic, phonon dispersion relation and thermodynamic properties of orthorhombic CaZrS$_3$ for optoelectronic applications
he correct estimation of thermal properties of ultra-scaled CMOS and thermoelectric semiconductor devices demands for accurate phonon modeling in such structures. This work provides a detailed description of the modified valence force field (MVFF) method to obtain the phonon dispersion in zinc-blende semiconductors. The model is extended from bulk to nanowires after incorporating proper boundary conditions. The computational demands by the phonon calculation increase rapidly as the wire cross-section size increases. It is shown that the nanowire phonon spectrum differ considerably from the bul…
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…
We employ inelastic helium atom-surface scattering to measure the low energy phonon dispersion along high-symmetry directions on the surface of the topological insulator Bi$_2$Te$_3$. Results indicate that one particular low-frequency branch experiences noticeable mode softening attributable to the interaction between Dirac fermion quasiparticles and phonons on the surface. This mode softening constitutes a renormalization of the real part of the phonon self-energy. We obtain the imaginary part, and hence lifetime information, via a Hilbert transform. In doing so we are able to calculate an av…
We report evidence of a non-adiabatic Kohn anomaly in boron-doped diamond, using a joint theoretical and experimental analysis of the phonon dispersion relations. We demonstrate that standard calculations of phonons using density functional perturbation theory are unable to reproduce the dispersion relations of the high-energy phonons measured by high-resolution inelastic x-ray scattering. On the contrary, by taking into account non-adiabatic effects within a many-body field-theoretic framework, we obtain excellent agreement with our experimental data. This result indicates a breakdown of the …
Hourglass dispersion is generally believed to be solely protected by nonsymmorphic symmetries, because these symmetries can introduce high-dimensional projective representations. Here, based on symmetry arguments, we propose that the hourglass dispersion can be jointly protected by symmorphic and nonsymmorphic symmetries, instead of the only conventional nonsymmorphic symmetry. Moreover, using first-principles calculations, we realize our proposal in phonon spectra of realistic materials that share an antiperovskite structure with space group \emph{P}4/\emph{nmm}. Importantly, the neck points …
We have used a shell model to study the phonon dynamics of multiferroic manganites RMnO3 (R= Tb, Dy, Ho). The calculated phonon dynamical properties, crystal structure, Raman frequencies and specific heat are found to be in good agreement with the available experimental data. Besides, the phonon density of states, elastic constants and phonon dispersion curves along high symmetry directions (sigma, delta and lambda) have also been computed. A zone-center imaginary Au mode is revealed in these phonon dispersion curves, which indicates the occurrence of metastability of the perovskite phase. The…
In this letter we report measurements of the coupling between Dirac fermion quasiparticles (DFQs) and phonons on the (001) surface of the strong topological insulator Bi2Se3. While most contemporary investigations of this coupling have involved examining the temperature dependence of the DFQ self-energy via angle-resolved photoemission spectroscopy (ARPES) measurements, we employ inelastic helium atom scattering to explore, for the first time, this coupling from the phonon perspective. Using a Hilbert transform, we are able to obtain the imaginary part of the phonon self-energy associated with…
Raman spectroscopy has become an essential technique to characterize and investigate graphene and many other two-dimensional materials. However, there still lacks consensus on the Raman signature and phonon dispersion of atomically thin boron nitride (BN), which has many unique properties distinct from graphene. Such a knowledge gap greatly affects the understanding of basic physical and chemical properties of atomically thin BN as well as the use of Raman spectroscopy to study these nanomaterials. Here, we use both experiment and simulation to reveal the intrinsic Raman signature of monolayer…
We develop a first-principles scheme to calculate adiabatic and non-adiabatic phonon frequencies in the full Brillouin zone. The method relies on the variational properties of a force-constants functional with respect to the first-order perturbation of the electronic charge density and on the localization of the deformation potential in the Wannier function basis. This allows for calculation of phonon dispersion curves free from convergence issues related to Brillouin zone sampling. In addition our approach justify the use of the static screened potential in the calculation of the phonon linew…
Recently discovered magnetic topological insulators $T$Bi$_{2}$Te$_{4}$ ($T=$Mn, Fe) crystallize into the $R\bar{3}m$ rhombohedral structure and exhibit the antiferromagnetic order. Here, we discuss the lattice dynamics of these compounds to confirm the stability of these systems. We show that the phonon dispersion does not contain soft modes, so both compounds are dynamically stable in the $R\bar{3}m$ phase. We perform theoretical analyses of the mode activity at $Γ$ point for the discussed compounds. In the case of the Raman active modes, our results are in agreement with the experimentally …
We report the first successful application of the {\it ab initio} quantum Monte Carlo (QMC) framework to a phonon dispersion calculation. A full phonon dispersion of diamond is successfully calculated at the variational Monte Carlo (VMC) level, based on the frozen-phonon technique. The VMC-phonon dispersion is in good agreement with the experimental results, giving renormalized harmonic optical frequencies very close to the experimental values, by significantly improving upon density functional theory (DFT) in the generalized gradient approximation. Key to success for the QMC approach is the s…
