Recent studies reveal that four-phonon scattering can be important in determining thermal conductivities of solids. However, these studies have been focused on materials where the thermal conductivity $\kappa$ is dominated by acoustic phonons, and the role of four-phonon scattering, although significant, is still smaller than that of three-phonon scattering at room temperature. In this work, taking AlSb as an example for which optical phonons contribute significantly to the thermal conductivity under the three-phonon picture, we demonstrate that four-phonon scattering can be more important than three-phonon scattering as it diminishes optical phonon thermal transport and therefore significantly reduces the thermal conductivities of materials. Also, our calculations show that four-phonon scattering can diminish the isotope effect on $\kappa$. Specifically, including four-phonon scattering reduces the room-temperature $\kappa$ of isotopically pure BAs from 3322 W/mK to 1721 W/mK, a $48\%$ reduction. Four-phonon scattering reduces the room-temperature $\kappa$ of the isotopically pure and naturally occurring AlSb by $70\%$ and $50\%$, respectively, indicating that four-phonon scattering is more important than three-phonon scattering. The reductions for isotopically pure and naturally occurring cubic GaN are about $34\%$ and $27\%$, respectively. For isotopically pure wurtzite GaN, the reduction is about $13\%$ at room temperature and $25\%$ at 400 K. These results provided important guidance for experimentalists for achieving high thermal conductivities in III-V compounds for applications in the semiconductor industry.

Extracting long-lasting performance from electronic devices and improving their reliability through effective heat management requires good thermal conductors. Taking both three- and four-phonon scattering as well as electron-phonon and isotope scattering into account, we predict that semimetallic $\theta$-phase tantalum nitride ($\theta \text{−}\mathrm{TaN}$) has an ultrahigh thermal conductivity ($\kappa$), of 995 and $\text{820\hspace{0.17em}\hspace{0.17em}}\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at room temperature along the $a$ and $c$ axes, respectively. Phonons are found to be the main heat carriers, and the high $\kappa$ hinges on a particular combination of factors: weak electron-phonon scattering, low isotopic mass disorder, and a large frequency gap between acoustic and optical phonon modes that, together with acoustic bunching, impedes three-phonon processes. On the other hand, four-phonon scattering is found to be significant. This study provides new insight into heat conduction in semimetallic solids and extends the search for high-$\kappa$ materials into the realms of semimetals and noncubic crystal structures.

The fundamental theory of Raman and infrared (IR) linewidth has been well established as the third-order lattice anharmonicity (three-phonon scattering). In this work, we use both rigorous density functional calculations and Raman experiments to find, surprisingly, that the fourth-order anharmonicity universally plays a significant or even dominant role over the third-order anharmonicity at room temperature, and more so at elevated temperatures, for a wide range of materials including diamond, Si, Ge, GaAs, boron arsenide (BAs), cubic silicon carbide ($3C\text{−}\mathrm{SiC}$), and $\alpha$-quartz. This is enabled by the large four-phonon scattering phase space of zone-center optical phonons. Raman measurements on BAs were conducted, and their linewidth verifies our predictions. The predicted infrared optical properties through the Lorentz oscillator model, after including four-phonon scattering, show much better agreement with experimental measurements than those three-phonon-based predictions. Our work advances the fundamental understanding of Raman and IR response and will broadly impact spectroscopy techniques and radiative transport.

Recently, first-principles calculations based on density functional theory have been widely used to predict the temperature-dependent infrared spectrum of polar materials, but the calculations are usually limited to the harmonic frequency (0 K) and three-phonon scattering damping for the zone-center infrared-active optical phonon modes, and fail to predict the high-temperature infrared optical properties of materials such as sapphire ($\alpha -{\text{Al}}_2{\text{O}}_3$), GaAs, $\text{Ti}{\text{O}}_2$, etc., due to the neglect of high-order phonon scattering damping and phonon frequency shift. In this work, we implemented first-principles calculations to predict the temperature-dependent infrared dielectric function of polar materials by including four-phonon scattering and phonon frequency shift. The temperature-dependent phonon damping by including three- and four-phonon scattering as well as the phonon frequency shift by including cubic and quartic anharmonicity and the thermal expansion effect are calculated based on anharmonic lattice dynamics method. The infrared dielectric function of $\alpha -{\text{Al}}_2{\text{O}}_3$ is parameterized, and then the temperature-dependent infrared optical reflectance is determined. We find that our predictions agree better with the experimental data than the previous density functional theory-based methods. This work will help to effectively predict the thermal radiative properties of polar materials at elevated temperature, which is generally difficult to measure, and will enable predictive design of new materials for radiative applications.

The Raman peak position and linewidth provide insight into phonon anharmonicity and electron-phonon interactions in materials. For monolayer graphene, prior first-principles calculations have yielded decreasing linewidth with increasing temperature, which is opposite to measurement results. Here, we explicitly consider four-phonon anharmonicity, phonon renormalization, and electron-phonon coupling, and find all to be important to successfully explain both the $G$ peak frequency shift and linewidths in our suspended graphene sample over a wide temperature range. Four-phonon scattering contributes a prominent linewidth that increases with temperature, while temperature dependence from electron-phonon interactions is found to be reversed above a doping threshold ($\hslash {\omega }_G/2$, with ${\omega }_G$ being the frequency of the $G$ phonon).

Phonon energies at finite temperatures shift away from their harmonic values due to anharmonicity. In this paper, we have realized the rigorous calculation of phonon energy shifts of silicon by three- and four-phonon scattering from first principles. The anharmonic fourth-order force constants are calculated by considering up to the fifth nearest neighbors. The results agree reasonably well with available data from inelastic neutron scattering throughout the Brillouin zone. Surprisingly, the frequency shifts of optical phonon modes near the $\mathrm{\Gamma }$ point are sensitive to the cutoff radius of the fourth-order force constants, in contrast to the four-phonon scattering rates, which nearly saturate when considering the second nearest neighbors. We have also compared the results with ab initio molecular dynamics simulations and found that the higher order of anharmonicity is important for optical phonons. Our work provides critical insight into the anharmonic phonon frequency shift and will have a significant impact on the thermal and optical applications.