Low-frequency Optical Phonon Modes Research Articles

Polymorphs of Titanium Dioxide: An Assessment of the Variants of Projector Augmented Wave Potential of Titanium on Their Geometric and Dielectric Properties.

Titanium dioxide (TiO2) is one of the important functional materials owing to its diverse applications in many fields of chemistry, physics, nanoscience, and technology. Hundreds of studies on its physicochemical properties, including its various phases, have been reported experimentally and theoretically, but the controversial nature of relative dielectric permittivity of TiO2 is yet to be understood. Toward this end, this study was undertaken to rationalize the effects of three commonly used projector augmented wave (PAW) potentials on the lattice geometries, phonon vibrations, and dielectric constants of rutile (R-)TiO2 and four of its other phases (anatase, brookite, pyrite, and fluorite). Density functional theory calculations within the PBE and PBEsol levels, as well as their reinforced versions PBE+U and PBEsol+U (U = 3.0 eV), were performed. It was found that PBEsol in combination with the standard PAW potential centered on Ti is adequate to reproduce the experimental lattice parameters, optical phonon modes, and the ionic and electronic contributions of the relative dielectric permittivity of R-TiO2 and four other phases. The origin of failure of the two soft potentials, namely, Ti_pv and Ti_sv, in predicting the correct nature of low-frequency optical phonon modes and ion-clamped dielectric constant of R-TiO2 is discussed. It is shown that the hybrid functionals (HSEsol and HSE06) slightly improve the accuracy of the above characteristics at the cost of a significant increase in computation time. Finally, we have highlighted the influence of external hydrostatic pressure on the R-TiO2 lattice, leading to the manifestation of ferroelectric modes that play a role in the determination of large and strongly pressure-dependent dielectric constant.

Delocalized Bi-tetrahedral cluster induced ultralow lattice thermal conductivity in Bi3Ir3O11

Low-frequency cluster vibration plays an important role in reducing the lattice thermal conductivity of a system. Here, we show a new type of cluster vibration called “delocalized cluster vibration” that involves a highly symmetric local structure with lone pair electrons and marked impacts on lattice thermal transport. We take a transition-metal oxide Bi3Ir3O11 (two specific Wyckoff positions for Bi: corner-Bi1 and inner-Bi2) as an example, which exhibits counterintuitive low lattice thermal conductivity in metallic materials. Based on first-principles simulations of phonon transport in the Boltzmann transport formulation, this study shows that the four fourth neighbor Bi2 atoms form a regular Bi-tetrahedral cluster (Bi24), which collectively vibrates in certain intercorrelated patterns strongly and induces low-frequency optical phonon modes (∼0.77 and ∼1.06 THz) along with low group velocities. The Bi24-related optical modes interrupt the acoustic vibrations and thus suppress the lattice thermal conductivity to an ultralow value (calculated value is 1.0 W/m·K at 300 K). Surprisingly, these Bi2–Bi2 have relatively large distances but significant interatomic force constants, indicating delocalized interactions among Bi24. This work demonstrates that the delocalized cluster vibration plays a significant role in lowering lattice thermal conductivity.

Optical phonon mode assisted thermal conductivity in p-type ZrIrSb half-Heusler alloy: a combined experimental and computational study

Half-Heusler (HH) alloys with an 18 valence electron count have attracted significant interest in the area of research related to thermoelectrics (TEs). Understanding the novel transport properties exhibited by these systems with semiconducting ground state is an important focus area in this field. The large thermal conductivity shown by most of the HH alloys poses a major hurdle to improving the figure of merit (ZT). In addition, understanding the mechanism of thermal conduction in heavy-constituent HH alloys is an interesting aspect. Here, we have investigated the high-temperature TE properties of ZrIrSb through experimental studies, phonon dispersion and electronic band structure calculations. ZrIrSb is found to exhibit a substantially lower magnitude of resistivity and Seebeck coefficient near room temperature due to the existence of anti-site disorder between Ir/Sb and vacant sites. Interestingly, in ZrIrSb, lattice thermal conductivity is governed by a coupling between the acoustic and low-frequency optical phonon modes, which originates due to heavier Ir/Sb atoms. This coupling leads to an enhancement in the Umklapp processes due to the optical phonon excitations near the zone boundary, resulting in a lower magnitude of κ L. Our studies point to the fact that the simultaneous existence of two heavy mass elements within a simple unit cell can substantially decrease the lattice degrees of freedom.

First principles study on the lattice dynamics and electron-phonon interaction of HfOs and HfRu compounds

From the first principles calculation based on the plane-wave pseudopotential method of density functional theory, and the linear response technique, we have performed electronic structure, phonon and electron-phonon interaction of superconducting compounds HfOs and HfRu in B2 phase. The distribution of energy with different wave vector in the first Brillouin zone and conductive charge carriers (electrons and holes) at Fermi level are described by the electronic band structure and Fermi surfaces (FS), which reveal that both the compounds are metallic in nature. Phonon dispersion curves along with phonon density of states for both the compounds are calculated. Moreover, for the convincement of phonon calculation, we have described the eigen vector displacement of optical phonon modes at the zone centre which reveals that the computed phonon spectra are real. The interaction of electron with acoustic phonon modes and low-frequency optical phonon modes is responsible for superconductivity for both the compounds. The detailed discussion of superconductivity is given in terms of Eliashberg spectral function (α2F(ω)), electron phonon coupling constants (λ) and superconducting transition temperature (TC). The calculated value of λ is 0.41 and 0.33 for HfOs and HfRu. Using Allen Dynes formula the calculated superconducting transition temperature is 1.16 K and 1.163 K, with good agreement of experimental values.

Localized dimers drive strong anharmonicity and low lattice thermal conductivity in ZnSe2

We calculate the lattice thermal conductivities of the pyrite-type ZnSe2 at pressures of 0 and 10 GPa using the linearized phonon Boltzmann transport equation. We obtain a very low value [0.69 W/(mK) at room temperature at 0 GPa], comparable to the best thermoelectric materials. The vibrational spectrum is characterized by the isolated high-frequency optical phonon modes due to the stretching of Se-Se dimers and low-frequency optical phonon modes due to the rotation of Zn atoms around these dimers. The low-frequency optical phonon modes are characterized by a strong anharmonicity and will substantially increase the three-phonon scattering space which suppress the thermal conductivity. Interestingly, two transverse acoustic phonon modes with similar frequencies and wave vectors have very different degrees of anharmonicity depending on their polarization. We relate this to the low thermal conductivity and show that the anharmonicities of the transverse acoustic phonon modes are connected to the corresponding change in the pyrite parameter, which can be interpreted as a descriptor for the local volume change. To determine the thermoelectric performance of ZnSe2, we also investigate its electrical transport properties. The results show that both p-type or n-type ZnSe2 can show promising electrical transport properties. We trace this back to the complex energy isosurfaces of both valence and conduction bands. The low thermal conductivities and promising electrical transport properties lead to a large thermoelectric figure of merit of ZnSe2 for both p-type and n-type doping.

Origins of significant reduction of lattice thermal conductivity in graphene allotropes

Coherent wave effects of thermal phonons hold promise of transformative opportunities in thermal transport control but remain largely unexplored due to the small wavelength of thermal phonons, typically below a few nanometers. This small length scale indicates that, instead of artificial phononic crystals, a more promising direction is to examine the coherent phonon effects in natural materials with hierarchical superstructures matching the thermal phonon wavelength. In this work, we use first-principles simulations to characterize the previously unstudied thermal properties of D-graphene and T-graphene, two-dimensional carbon allotropes based upon the traditional graphene structure but containing a secondary, in-plane periodicity. We find that despite very similar atomic structure and bonding strength, D-graphene and T-graphene possess significantly different thermal properties than that of pristine graphene. At room temperature, the calculated thermal conductivity of D-graphene and T-graphene is 600 Wm-1K-1 and 800 Wm-1K-1 compared to over 3000 Wm-1K-1 for graphene. We attribute these distinct properties to the presence of naturally occurring, low frequency optical phonon modes that display characteristics of phonon coherence and arise from a folding of the acoustic modes and the associated frequency gap opening, a phenomenon also found in superlattices where an out of plane periodicity is introduced. Furthermore, we observe significantly enhanced Umklapp scatterings in D- and T-graphene that largely suppress the hydrodynamic phonon transport in pristine graphene. Our study presents D-graphene and T-graphene as ideal model systems to explore the coherent phonon effects in 2D and demonstrates the potential of using coherent phonon effects to significantly modify thermal transport of 2D materials without making drastic changes to their fundamental compositions.

Pressure dependence of the superconducting transition temperature of compressed LaH10

Two recent experiments [M. Somayazulu et al. Phys. Rev. Lett. 122, 027001 (2019) and A. P. Drozdov et al., Nature (London) 569, 528 (2019)] reported the discovery of superconductivity in the fcc phase of ${\mathrm{LaH}}_{10}$ at a critical temperature ${T}_{\mathrm{c}}$ between $250\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}260\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ under a pressure of about 170 GPa. However, the dependence of ${T}_{\mathrm{c}}$ on pressure showed different patterns, i.e., the former experiment observed a continuous increase of ${T}_{\mathrm{c}}$ up to $\ensuremath{\sim}275\phantom{\rule{0.28em}{0ex}}\mathrm{K}$ on further increase of pressure to 202 GPa, while the latter one observed an abrupt decrease of ${T}_{\mathrm{c}}$ with increasing pressure. Here, based on first-principles calculations, we reveal that for the $\mathrm{fcc}\ensuremath{-}{\mathrm{LaH}}_{10}$ phase, softening of the low-frequency optical phonon modes of H atoms dramatically occurs as pressure decreases, giving rise to a significant increase of the electron-phonon coupling (EPC) constant. Meanwhile, the electronic band structure near the Fermi energy is insensitive to change with respect to pressure. These results indicate that the pressure-dependent phonon softening is unlikely associated with Fermi-surface nesting, but driven by effective screening with the electronic states near the Fermi energy. It is thus demonstrated that the strong variation of EPC with respect to pressure plays a dominant role in the decrease of ${T}_{\mathrm{c}}$ with increasing pressure, supporting the measurements of Drozdov et al.

Theoretical investigation of the superconductivity mechanism of BaIr2As2

Based on first-principles pseudopotential plane-wave method within the generalised gradient approximation, I have studied the structural, electronic, vibrational and BCS superconducting properties of BaIr2As2. The calculated electronic structure and density of states suggest that the bonding is a combination of covalent, ionic and metallic in nature and that the Fermi level falls in one of the peaks in the electronic density of states. The electron–phonon interaction calculations suggest that the mechanism for superconductivity is heavily governed by interactions of electrons with acoustic phonon modes and low-frequency optical phonon modes. By integrating the Eliashberg spectral function, the value of average electron–phonon coupling parameter is found to be 0.64 and the superconducting critical temperature is calculated to be 2.337 K, in excellent agreement with the experimentally reported value of 2.450 K.

Phonon transport properties of two-dimensional electride Ca2N—A first-principles study

We investigate phonon transport in dicalcium nitride (Ca2N), an electride with two-dimensional confined electron layers, using first-principles density functional theory and the phonon Boltzmann transport equation. The in-plane (κ100) and out-of-plane (κ001) lattice thermal conductivities at 300 K are found to be 11.72 W m−1 K−1 and 2.50 W m−1 K−1, respectively. Spectral analysis of lattice thermal conductivity shows that ∼85% of κ100 and κ001 is accumulated by phonons with frequencies less than 5.5 THz and 2.5 THz, respectively. Modal decomposition of lattice thermal conductivity further reveals that the optical phonons contribute to ∼68% and ∼55% of overall κ100 and κ001, respectively. Phonon dispersion suggests that the large optical phonon contribution is a result of low frequency optical phonons with high group velocities and the lack of phonon bandgap between the acoustic and optical phonon branches. We find that the optical phonons with frequencies below ∼5.5 THz have similar three-phonon phase space and scattering rates as acoustic phonons. Comparison of the contributions from emission and absorption processes reveals that the three-phonon phase space and scattering rates of phonons—optical or acoustic—with frequencies below 5.5 THz are largely dominated by absorption processes. We conclude that the large contribution to lattice thermal conductivity by optical phonons is due to the presence of multiple low frequency optical phonon modes with high group velocities and similar phase space and scattering rates as the acoustic phonons. This study provides the frequency and temperature dependent lattice thermal conductivity and insights into phonon transport in Ca2N, both of which have important implications for the development of Ca2N based devices.

Electron–phonon interaction and superconductivity in the borocarbide superconductor

We have made an ab initio investigation of electron–phonon interaction and superconductivity in the borocarbide super-conductor adopting the body-centred tetragonal -type of layered crystal structure. The calculated electronic structure and density of states suggest that the bonding is a combination of covalent, ionic and metallic in nature and that the Fermi level falls in one of the peaks in the electronic density of states. Our electron–phonon interaction calculations suggest that the mechanism for superconductivity is heavily governed by interactions of electrons with acoustic phonon modes and low-frequency optical phonon modes, which strongly modulate tetrahedral bond angles. By integrating the Eliashberg spectral function, the value of average electron–phonon coupling parameter is found to be 0.93 and the superconducting critical temperature is calculated to be 16.28 K, in excellent agreement with the experimentally reported value of 16.0 K.

Physical properties of the body-centred tetragonal

We have investigated the structural, elastic, electronic, and lattice dynamical properties of in the body-centred tetragonal structure using a generalised gradient approximation of the density functional theory and the ab initio pseudopotential method. The calculated second-order elastic constants indicate that is mechanically stable and behaves in a ductile manner. Our electronic results show that the states close to the Fermi level are primarily contributed by Pd d and Ge p orbitals. A detailed analysis of electron–phonon interaction calculations reveals that the mechanism for superconductivity in is mainly governed by interactions of Pd d and Ge p electrons around the Fermi level with acoustic phonon modes and low-frequency optical phonon modes, which strongly change PdGe tetrahedral bond angles. The values of the average electron–phonon coupling constant and the logarithmic average frequency are calculated to be 0.66 and 77.3 K, respectively. Inserting these values into the Allen–Dynes formula with using an acceptable value of for the effective Coulomb repulsion parameter, the value of superconducting transition temperature is obtained to be 1.69 K, which is in excellent agreement with its experimental value.

The strain effect on superconductivity in phosphorene: a first-principles prediction

The effects of biaxial and uniaxial strains on electron–phonon coupling and superconductivity in monolayer phosphorene are systematically investigated by first-principles calculations. It is found that the electron–phonon coupling primarily comes from the low frequency optical phonon modes around , and the biaxial strain gives rise to more a obvious increase in density of states around the Fermi level and phonon softening in the low frequency regime compared to the other two types of uniaxial strain. Therefore, the electron–phonon coupling is more significantly enhanced by the biaxial strain than the uniaxial strains and the superconducting transition temperature Tc increases sharply from 3 K to 16 K at the typical doping concentration n2D = 3.0 × 1014cm−2 when the biaxial strain reaches 4.0%.

Enhancement of thermoelectric performance in InAs nanotubes by tuning quantum confinement effect

By using the nonequilibrium Green's function method, we study the thermoelectric properties of InAs nanotubes. The results show that InAs nanotube with a certain internal diameter has much higher ZT value than nanowire due to the enhancement of quantum confinement effect leading to the increase of the power factor S2G. The ZT value of InAs nanotube can reach 1.74, which is about three times greater than that of nanowires. Moreover, it is found that the ZT values of InAs nanotubes decrease rapidly with the increase of internal diameter, which results from the rapid increase of phonons thermal conductance due to the “red shift” of low-frequency optical phonon modes.

Symmetry, mechanism of the pairing, and the isotope effect in the cuprates

This paper is concerned mainly with the problem of the origin of highTc.s-Wave vs.d-wave pairing, the isotope effect, and the strong coupling of the carriers to low-frequency optical phonon modes are discussed. This latter strong coupling is sufficient to provide highTc.