Phonon Dispersion Relations Research Articles

First- and second-order Raman spectroscopy of monoclinic β−Ga2O3

We employ a combined experimental-theoretical study of the first- and second-order Raman modes of monoclinic $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. Gallium oxide has attracted considerable interest due to its deep-UV band gap paired with a high critical field strength, offering promising applications in power electronics. A crucial prerequisite for the future development of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$-based devices is a detailed understanding of the lattice vibrations, i.e., phonons, as they govern important material properties such as elasticity, thermal conductivity, temperature-dependence of the band gap, or free-carrier transport. Polarized micro-Raman spectroscopy measurements on the (010) and ($\overline{2}01$) planes of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ single crystals enable the determination of the phonon frequencies of all 15 first-order and more than 40 second-order Raman modes. The experimental results are correlated with calculations of the mode frequencies, the phonon dispersion relation, and the phonon density of states using density functional perturbation theory. By applying a group-theoretical analysis, we are able to distinguish between overtones and combinational modes and identify the high-symmetry points in the Brillouin zone that contribute to the observed second-order modes. Based on this information, we demonstrate the simultaneous determination of Raman, IR, and acoustic phonons in $\ensuremath{\beta}\ensuremath{-}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ by second-order Raman spectroscopy.

Monte-Carlo modeling of phonon thermal transport using DFT-based anisotropic dispersion relations over the full Brillouin zone

We present a Monte Carlo (MC) approach to solve the phonon Boltzmann transport equation (BTE) in which the anisotropic phonon dispersion relations over the full Brillouin zone (BZ) are used. In this approach, the discretization of the BZ used to compute the phonon relaxation time places constraints on the direction of scattered phonons in the real-space simulation domain. The phonon dispersion and phonon relaxation times are calculated using the density functional theory (DFT) approach. The modified MC approach is validated by a close examination of its ability to simulate phonon transport in both the ballistic and diffusive regimes for multiple materials including GaAs, InAs, ThO2, and α-U. In doing so, the phonon thermal conductivities from 100 K to 1000 K are calculated and compared with traditional non-transport solution of the phonon BTE. It is found that the phonon thermal conductivities of α-U and ThO2 obtained from MC simulations using isotropic dispersion are larger than the values obtained using anisotropic phonon dispersion relations over the full BZ. The effect of phonon-defect scattering on the thermal conductivity of ThO2 is also studied as an application of the current MC approach and found to agree with previously computed values in the literature. The MC solver developed here has been parallelized as a step to demonstrate its potential to solving computationally intensive phonon thermal transport problems at the mesoscale.

Thermal conductivity and phonon scattering of AlGaN nanofilms by elastic theory and Boltzmann transport equation

Aluminum gallium nitride (AlGaN) plays an essential role in deep ultra-violet light emitting diodes and high electron mobility transistors etc. For example, 2 nm – 5 nm AlGaN nanofilms consist of the quantum wells in ultra-violet light emitting diodes, which have been attracting extensive attention since the rise of COVID 2019. Since most photons and heat are generated in these AlGaN nanofilms, the thermal properties of AlGaN nanofilms are strongly influenced by the heat dissipation of devices. In this paper, utilizing elastic theory and the Boltzmann transport equation, the phonon dispersion relations, density of states, specific heat capacities and thermal conductivities of 2 nm Al δ Ga1−δ N nanofilms with various δ are theoretically calculated at different temperatures. The thermal conductivity of nanofilm is significantly smaller than that of its bulk counterpart. In contrast with bulk AlGaN, due to the dominance of boundary scattering and alloy disorder scattering, the thermal conductivity of Al δ Ga1−δ N exhibits a similar dependence on Al concentration to bulk Al δ Ga1−δ N. Meanwhile, since the screening of Umklapp scattering, the saturation temperature of thermal conductivity is delayed from 50 to 100 K in bulks to about 300 K in nanofilms. The shrinkage of nanofilms’ thermal conductivity is also slower than for bulks. We believe that our work will be helpful in controlling the self-heating effect of devices based on AlGaN nanofilms.

Spin-Peierls Distortion of TiPO4 Causing a Transition from a Magnetic to a Nonmagnetic Insulating State and Its Effect on the Thermoelectric Properties: Density Functional Theory Analysis.

Density functional theory calculations were carried out to probe the nature of the electronic structure change in TiPO4 before and after its spin-Peierls distortion at 74.5 K, which is characterized by the dimerization in the chains of Ti3+ (d1) ions present in TiPO4. These calculations suggest strongly that the electronic state of TiPO4 is magnetic insulating before the distortion, but becomes nonmagnetic insulating after the distortion. Consistent with this suggestion, the phonon dispersion relations calculated for TiPO4 show that the undistorted TiPO4 is stable, while the distorted TiPO4 is not, if each Ti3+ ion has a spin moment, and that the opposite is true if each Ti3+ ion has no spin moment. These observations suggest that the driving force for the spin-Peierls distortion is the formation of direct metal-metal bonds leading to the dimerized chains of Ti3+ ions. The abrupt change in the electronic structures from a magnetic insulating state to a nonmagnetic insulating state explains why the spin-Peierls distortion of TiPO4 exhibits a first-order character. Although the two electronic states of TiPO4 before and after the distortion have a band gap, the substantial spin-Peierls distortion is found to enhance the thermoelectric properties of TiPO4.

Ab initio investigations of electronic structure, mechanical properties, phonon stability, and thermodynamics of the Mg–Er system

We report the results of a first principles study of electronic structure, elastic properties, ideal strengths, phonon stability and thermodynamic properties of the Mg–Er system. The calculations have been carried out within density-functional theory (DFT) and density-functional perturbation theory (DFPT) frameworks. The calculated lattice constants, cell volumes, bulk moduli and their pressure derivations, as well as formation enthalpies are in good agreement with the existing experimental and theoretical data. The single-crystal elastic constants and polycrystalline moduli were derived from the energy-strain relationships and Hill model, we show that Pm-3m-MgEr, I-43m-Mg24Er5, and I4/mmm-MgEr2 systems are all thermodynamically and mechanically stability. The ideal tensile and shear strengths of three phases have been evaluated from first-principles method. Especially, the phonon dispersion relations and densities of states of Pm-3m-MgEr, I-43m-Mg24Er5, and I4/mmm-MgEr2 alloys are investigated systematically from the linear response method of DFPT. Furthermore, the Raman-active and Infrared-active phonon modes at the center of Brillouin Zone (BZ) have been assigned combining with the factor group theory. Our calculated results indicate that three magnesium-erbium phases are also all dynamically stable. Accordingly, within the calculated phonon vibrations and quasi-harmonic Debye model, the vibration entropy and the lattice heat capacity of three phases have also been predicted.

Electronic Properties and Lattice Dynamics of LixCoO2 and NaxCoO2 (x = 0, 0.5, 1) Studied by Hybrid Density Functional Theory

A systematic hybrid density functional theory study on the electronic and vibrational properties of MxCoO2 compounds with M = Li, Na and is reported. The used DFT‐PBE0 method describes the structural parameters of the studied compounds well in comparison to experimental data. All studied magnetic species are treated as ferromagnets and the Co(IV) atoms possess a magnetic moment of 1.2 μB. At 0 K, favors a monoclinic structure very close to trigonal symmetry and behaves as a Mott insulator. The electronic bandgap increases as x increases from 0 to 1. The simulated infrared and Raman spectra together with full phonon dispersion relations show that the intercalation of Li and Na ions affects the lattice dynamics of CoO2 in a different way.

Anisotropic mechanical response, high negative thermal expansion, and outstanding dynamical stability of biphenylene monolayer revealed by machine-learning interatomic potentials

Recently, the two-dimensional (2D) biphenylene network with a specific arrangement of four-, six-, and eight-membered carbon rings has been fabricated over the gold surface via a two-step polymerization technique (Science 372(2021), 852). Inspired by the aforementioned experimental advance and exciting physics of full-carbon 2D lattices, for the first time, we herein employ machine-learning interatomic potentials (MLIPs) to explore the mechanical properties, failure behavior, dynamical stability, and thermal expansion of the biphenylene monolayer. The remarkable accuracy of the developed MLIP-based models is concluded by comparing the predicted direction-dependent uniaxial stress-strain relations and failure mechanism of the biphenylene monolayer with those obtained by density functional theory simulations. Analysis of phonon dispersion relations reveals an outstanding dynamical stability of the biphenylene monolayer. Similarly to graphene, the biphenylene network also exhibits a negative thermal expansion, but with around twice the value of graphene at room temperature. We also studied the temperature effect on the tensile strength and failure strain of the biphenylene monolayer. The presented results provide a useful vision concerning the thermo-mechanical properties of the 2D biphenylene network.

Ultralow lattice thermal conductivity and high thermoelectric performance of the WS2/WTe2 van der Waals superlattice

Vertically stacked materials have received much attention due to the possibilities of effective modulation of their electronic and transport properties. In this work, we combine first-principles calculations and Boltzmann theory to investigate the thermoelectric properties of the van der Waals superlattice formed by alternately stacking the WS2 and WTe2 layers along the out-of-plane direction. Both the ab-initio molecular dynamics simulation and the phonon dispersion relations indicate that the superlattice structure is rather stable. Compared with those of the bulk WS2 and WTe2, our system exhibits much lower interlayer lattice thermal conductivity originated from the mixed covalent and van der Waals bonding. Besides, the weaker energy dispersions and higher band degeneracy along the out-of-plane direction lead to a larger power factor, which in turn gives a significantly enhanced ZT value of ∼2.4 at 800 K. Collectively, our theoretical work demonstrates the great advantage of engineering layered structure for thermoelectric applications.

The phase diagrams of beryllium and magnesium oxide at megabar pressures

We perform ab initio simulations of beryllium (Be) and magnesium oxide (MgO) at megabar pressures and compare their structural and thermodynamic properties. We make a detailed comparison of our two recently derived phase diagrams of Be (Wu et al 2021 Phys. Rev. B 104 014103) and MgO (Soubiran and Militzer 2020 Phys. Rev. Lett. 125 175701) using the thermodynamic integration technique, as they exhibit striking similarities regarding their shape. We explore whether the Lindemann criterion can explain the melting temperatures of these materials through the calculation of the Debye temperature at high pressure. From our free energy calculations, we find that the melting line of both materials is well represented by the Simon–Glazel fit T m(P) = T 0(1 + P/a)1/c , where T 0 = 1564 K, a = 15.8037 GPa and c = 2.4154 for Be, while T 0 = 3010 K, a = 10.5797 GPa and c = 2.8683 for the MgO in the B1. For the B2 phase, we use the values a = 26.1163 GPa and c = 2.2426. Both materials exhibit negative Clapeyron slopes on the boundaries between the two solid phases that are strongly affected by anharmonic effects, which also influence the location of the solid–solid–liquid triple point. We find that the quasi-harmonic approximation underestimates the stability range of the low-pressure phases, namely hcp for Be and B1 for MgO. We also compute the phonon dispersion relations at low and high pressure for each of the phases of these materials, and also explore how the phonon density of states is modified by temperature. Finally, we derive secondary shock Hugoniot curves in addition to the principal Hugoniot curve for both materials, and study their offsets in pressure between solid and liquid branches.

Anharmonic lattice dynamics in large thermodynamic ensembles with machine-learning force fields: CsPbBr3 , a phonon liquid with Cs rattlers

The phonon dispersion relations of crystal lattices can often be well-described with the harmonic approximation. However, when the potential energy landscape exhibits more anharmonicity, for instance, in case of a weakly bonded crystal or when the temperature is raised, the approximation fails to capture all crystal lattice dynamics properly. Phonon-phonon scattering mechanisms become important and limit the phonon lifetimes. We take a novel approach and simulate the phonon dispersion of a complex dynamic solid at elevated temperatures with Machine-Learning Force Fields of near-first-principles accuracy. Through large-scale molecular dynamics simulations the projected velocity autocorrelation function (PVACF) is obtained. We apply this approach to the inorganic perovskite CsPbBr$_{3}$. Imaginary modes in the harmonic picture of this perovskite are absent in the PVACF, indicating a dynamic stabilization of the crystal. The anharmonic nature of the potential makes a decoupling of the system into a weakly interacting phonon gas impossible. The phonon spectra of CsPbBr$_{3}$ show the characteristics of a phonon liquid. Rattling motions of the Cs$^{+}$ cations are studied by self-correlation functions and are shown to be nearly dispersionless motions of the cations with a frequency of $\sim$0.8THz within the lead-bromide framework.

Revisiting phonon transport in perovskite SrTiO3 : Anharmonic phonon renormalization and four-phonon scattering

We investigate the role of anharmonic phonon renormalization and four-phonon scattering in the thermal transport of cubic ${\mathrm{SrTiO}}_{3}$ from 200 to 800 K by constructing an accurate first-principles machine-learning potential with active learning. The anharmonic phonon dispersion relations show obvious low-frequency phonon hardening as temperature increases, implying potential importance of fourth order lattice anharmonicity in cubic ${\mathrm{SrTiO}}_{3}$. Under the perturbation theory and Boltzmann transport equation scheme, we find that phonon frequency renormalization can make a significant improvement in the calculations of thermal conductivity and its temperature dependence of cubic ${\mathrm{SrTiO}}_{3}$ compared to experimental data. Four-phonon scattering is usually important in strongly anharmonic materials with ultralow thermal conductivity and simple crystals featured by large acoustic-optical phonon band gaps. Nonetheless, we find that four-phonon scattering can make a considerable contribution to suppressing phonon transport in cubic ${\mathrm{SrTiO}}_{3}$ which has a moderate thermal conductivity. This study deepens the understanding of anharmonic phonon renormalization and four-phonon scattering in oxide perovskites.

Pressure induced structural phase transitions of technologically significant mercurous chloride at room temperature: An account from first-principle DFT and Born–Oppenheimer molecular dynamics studies

This paper reports for the first time an in-depth study based on first-principle calculations to unveil the underlying physics that governs the pressure induced structural phase transitions of Hg2Cl2 compound at room temperature. The phonon dispersion relations and phonon density of states have been critically explored for the tetragonal and orthorhombic phases of the compound to unveil the phonon modes associated with the phase transitions. The nature of the phase transition whether it is “displacive” or of “order–disorder” type has also been explored. We believe that the present study based on density functional theory and Born–Oppenheimer molecular dynamics calculations will help understand the underlying physics behind the above referred phase transitions and the anisotropic behavior of the compound, which in turn bears technologically significant relevance for its applications in optoelectronic devices, acousto-optic tunable filters, and in fiber-optic communication systems.

Polaron Models with Regular Interactions at Strong Coupling

We study a class of polaron-type Hamiltonians with sufficiently regular form factor in the interaction term. We investigate the strong-coupling limit of the model, and prove suitable bounds on the ground state energy as a function of the total momentum of the system. These bounds agree with the semiclassical approximation to leading order. The latter corresponds here to the situation when the particle undergoes harmonic motion in a potential well whose frequency is determined by the corresponding Pekar functional. We show that for all such models the effective mass diverges in the strong coupling limit, in all spatial dimensions. Moreover, for the case when the phonon dispersion relation grows at least linearly with momentum, the bounds result in an asymptotic formula for the effective mass quotient, a quantity generalizing the usual notion of the effective mass. This asymptotic form agrees with the semiclassical Landau–Pekar formula and can be regarded as the first rigorous confirmation, in a slightly weaker sense than usually considered, of the validity of the semiclassical formula for the effective mass.

Measuring phonon dispersion at an interface.

The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface1. These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device2. Although related theoretical work began decades ago1,3-5, experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics.

Softening of the Euler Buckling Criterion under Discretization of Compliance

The classical buckling problem, studied by Euler himself, is still important in many fields where macroscale or nanoscale structures may fail under compression. The impact of discrete or atomic structure on the critical buckling load is of paramount interest, yet the physics is still insufficiently understood. This study combines experiment and theory to solve that enigma: Phonon dispersion relations are at the heart of the physics of the buckling of both discrete and continuous structures. This insight will have an impact on engineering solutions, from nanostructures where molecular details prevail, to medical stents that naturally feature discretized polygonal symmetry.

An optical lattice with sound.

Quantized sound waves-phonons-govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (for example, by binding electrons into superconducting Cooper pairs)1-3. The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff4. Optical-lattice realizations of crystals therefore lack some of the central dynamical degrees of freedom that determine the low-temperature properties of real materials. Here, we create an optical lattice with phonon modes using a Bose-Einstein condensate (BEC) coupled to a confocal optical resonator. Playing the role of an active quantum gas microscope, the multimode cavity QED system both images the phonons and induces the crystallization that supports phonons via short-range, photon-mediated atom-atom interactions. Dynamical susceptibility measurements reveal the phonon dispersion relation, showing that these collective excitations exhibit a sound speed dependent on the BEC-photon coupling strength. Our results pave the way for exploring the rich physics of elasticity in quantum solids, ranging from quantum melting transitions5 to exotic 'fractonic' topological defects6 in the quantum regime.

Developing machine learning potential for classical molecular dynamics simulation with superior phonon properties

Classical molecular dynamics is one of the most important methods for exploring material properties and uncovering physical mechanism, but the predicted results strongly depend on the used potentials. Using ab initio molecular dynamics simulations to obtain atomic conformations and the associated energy and force as training set and testing set, we developed a Gaussian approximation potential model for single-layer MoS2based on the machine learning method. The phonon dispersion relations calculated from the developed potential are compared well to that of density functional theory,which confirms the accuracy of the developed potential in the harmonic interaction. We also calculated the temperature-dependent Raman-active phonon frequency and linewidth of the single-layer MoS2 using classical molecular dynamics. The obtained temperature-dependent phonon frequency and linewidth are compared with the corresponding experimental results, indicating that the developed potential still has high accuracy in the anharmonic interactions. The detailed process and methods to obtain the MoS2potential in this work can be extended and applied to the development and investigation of the high-precision potential of emerging new materials.

Deformation potential extraction and computationally efficient mobility calculations in silicon from first principles

We present a first-principles framework to extract deformation potentials in Silicon based on density-functional theory (DFT) and density-functional perturbation theory (DFPT). We compute the electronic band structures, phonon dispersion relations, and electron-phonon matrix elements to extract deformation potentials for acoustic and optical phonons for all possible processes. The matrix elements clearly show the separation between intra- and inter-valley scattering in the conduction band, and quantify the strength of the scattering events in the degenerate bands of the valence band. We then use an advanced numerical Boltzmann transport equation (BTE) simulator that couples DFT electronic structures and energy/momentum-dependent scattering rates to compute the transport properties for electrons and holes. By incorporating ionized impurity scattering as well, we calculate the n-type and p-type mobility versus carrier density and make comparisons to experiments, indicating excellent agreement. The fact that the method we present uses well-established theoretical tools and requires the extraction of only a limited number of matrix elements, makes it generally computationally very attractive, especially for semiconductors with a large unit cell and lower symmetry.

Study of structural, electronic and magnetic properties of Ti doped Co2FeGe Heusler alloy: Co2Fe1−x Ti x Ge (x = 0, 0.5, and 0.75)

Tunability of structural, magnetic and electronic properties of Co2FeGe Heusler alloy is experimentally demonstrated by doping Ti in the Fe site (i.e. Co2Fe1−x Ti x Ge), followed by in-depth first principle calculations. Co2FeGe in its pure phase shows very high saturation magnetization, Curie temperature and spin-wave stiffness constant which were reported in our earlier work. With gradual increase in Ti doping concentration (x = 0.5 and 0.75), the experimental saturation magnetization is found to be decreased to 4.3 μ B/f.u. and 3.1 μ B/f.u. respectively as compared to the parent alloy (x = 0) having the saturation magnetization of 6.1 μ B/f.u. Variation of spinwave stiffness constant is also studied for different x and found to be decreasing from peak value of 10.4 nm2 meV (for x = 0) to the least value of 2.56 nm2 meV for x = 0.5. Justification of the experimental results is given with first principle calculations. Computational phase diagram of the alloys is found in terms of formation energy showing that the doping in Fe site (i.e. Co2Fe1−x Ti x Ge) is more stable rather than in Co site (i.e. Co2−x FeTi x Ge). The change in magnetic moment and half-metallicity with Ti doping concentration is better explained under GGA + U approach as compared to GGA approach signifying that the electron–electron correlation (U) has a distinct role to play in the alloys. Effect of variation of U for Ti atom is studied and optimized with reference to the experimental results. The dynamical stability of the Co2Fe1−x Ti x Ge alloy crystal structure is explained in terms of phonon dispersion relations and the effect of U on the phonon density of states is also explored. Close agreement between the experimental and theoretical results is observed.

Atomic mass dependency of a localized phonon mode in SiGe alloys

Using molecular dynamics, the effect of an atomic mass difference on a localized phonon mode in SiGe alloys was investigated. Phonon dispersion relations revealed that a change in atomic mass causes the optical and acoustic modes to shift frequency. The results indicate that the local mode is sensitive to both Si and Ge atomic mass changes; reducing the Si atomic mass shifts the local mode to higher frequencies, and increasing the Ge atomic mass shifts the local mode to lower frequencies. Furthermore, the results suggest that the local mode originates from the Si–Ge bond vibration. Although the Si–Si, Si–Ge, and Ge–Ge optical mode frequencies are well approximated by the two-body harmonic oscillator model, a much heavier effective mass than that of the Si–Ge pair must be assumed to reproduce the local mode frequency. A plausible interpretation of the local mode is a collective vibration of Ge clusters embedded within the Si lattice.