Analyzing the Role of Anharmonicity and Renormalization on Predicting Phonon Transport Properties in Crystals

Understanding the phonon properties of complex crystals with strong anharmonicity is important for their potential applications in the areas of thermal management, energy conversion, and sensing. Both intrinsic factors, such as mass ratio and asymmetricity of force field in a crystal, and extrinsic factors, such as temperature and pressure, determine the anharmonicity. Theoretically predicting phonon frequency and lifetime is further complicated when the force field is strongly asymmetric or the external field is relatively large where the harmonic approximation is invalid. Phonon renormalization is often needed to correctly consider the role of phonon anharmonicity in the materials. In this work, we used single crystals Si, CdTe, and PbTe as benchmarks to numerically investigate the effects of both intrinsic and extrinsic factors on phonon anharmonicity. To understand the anharmonicity of material systems, dispersion curve, energy of phonon modes, and Grüneisen parameter are usually investigated in both experiment and simulation methods. In addition to these phonon properties, we found that phonon eigenvectors, that are usually neglected in the past, provide another fundamental perspective of atomic vibrations to understand and explain the effect of anharmonicity in material systems. This analysis uses the amplitude ratio and vector angles between elements in the primitive cell defined from phonon eigenvectors of these materials with different anharmonicity. For the intrinsic factors, we compared the effect of mass ratio and asymmetricity of force field and found that the latter has a more profound effect on the phonon anharmonicity.  For the extrinsic factors, with an increasing temperature and pressure, not only the phonon frequencies but also the phonon eigenvectors will gradually change. Compared to the methods that explicitly consider the higher-order force constants to include the strong anharmonicity, the phonon renormalization method was adopted here to investigate the effect of anharmonicity on phonon frequency and lifetime. Three representative methods of phonon renormalization, time-domain normal mode analysis, spectral energy density method (frequency-domain normal mode analysis), and temperature effective potential method, were applied and compared. PbTe was used as a complex crystal model to compare phonon renormalization methods at different temperatures and pressures. We applied these methods using the same molecular dynamics settings, such as force field and atomic information, as the input for phonon renormalization. Phonon lifetimes directly calculated from the zero-Kevin third-order force constants are set as reference values to show the necessity of phonon renormalization. By conducting phonon renormalization with different methods, practical suggestions in processing details were provided for efficiently and accurately evaluating phonon properties in crystals with strong anharmonicity.