Self-consistent phonon calculations of lattice dynamical properties in cubic SrTiO$_{3}$ with first-principles anharmonic force constants (1506.01781v3)

Abstract: We present an \textit{ab initio} framework to calculate anharmonic phonon frequency and phonon lifetime that is applicable to severely anharmonic systems. We employ self-consistent phonon (SCPH) theory with microscopic anharmonic force constants, which are extracted from density-functional calculations using the least absolute shrinkage and selection operator technique. We apply the method to the high-temperature phase of SrTiO${3}$ and obtain well-defined phonon quasiparticles that are free from imaginary frequencies. Here we show that the anharmonic phonon frequency of the antiferrodistortive mode depends significantly on the system size near the critical temperature of the cubic-to-tetragonal phase transition. By applying perturbation theory to the SCPH result, phonon lifetimes are calculated for cubic SrTiO${3}$, which are then employed to predict lattice thermal conductivity using the Boltzmann transport equation within the relaxation-time approximation. The presented methodology is efficient and accurate, paving the way toward a reliable description of thermodynamic, dynamic, and transport properties of systems with severe anharmonicity, including thermoelectric, ferroelectric, and superconducting materials.

• The paper introduces a self-consistent phonon framework to compute anharmonic lattice dynamics in cubic SrTiO₃ using DFT and LASSO.
• It demonstrates that anharmonic phonon frequencies and lifetimes computed via SCPH provide accurate estimates of lattice thermal conductivity.
• The study emphasizes using extended supercells and sparse higher-order force constants extraction to overcome limitations of harmonic approximations.

Self-Consistent Phonon Calculations in Cubic SrTiO$_{3}$

The paper by Tadano and Tsuneyuki introduces a robust ab initio framework aiming to compute the anharmonic phonon properties of SrTiO$_{3}$, a prominent ferroic material. The framework employs a self-consistent phonon (SCPH) theory with anharmonic force constants derived from density functional theory (DFT), applying the least absolute shrinkage and selection operator (LASSO) to ensure a sparse and efficient parameter set.

In their methodology, the authors address the lattice dynamics in cubic SrTiO$_{3}$, particularly its high-temperature phase. Using SCPH, they obtain phonon quasiparticles that are free from the imaginary frequencies typically present in harmonic approximations. The ab initio calculations allow for predicting both anharmonic phonon frequencies and lifetimes, subsequently used to estimate the lattice thermal conductivity. The latter is calculated by solving the Boltzmann transport equation under the relaxation time approximation, which is necessary for computing the thermal properties of materials exhibiting severe anharmonicity.

A key result is the observation that anharmonic phonon frequencies, especially of the antiferrodistortive mode, display a strong dependence on supercell size near the critical temperature, emphasizing the importance of considering extended supercells in such calculations. The anharmonic contributions are effectively captured, showcasing the SCPH theory's ability to surpass limitations inherent to perturbative approaches, which often fail in highly anharmonic systems.

The computational approach applies LASSO to refine the higher-order force constants up to the sixth order. This systematic extraction avoids overfitting by only considering significant interactions within a large pool of potential parameters. Such a sparse representation efficiently models the anharmonic potential energy surface, essential for accurate dynamical and thermodynamic predictions.

The paper distinctly contributes to the theoretical examination of lattice dynamical properties in materials with complex interactions, providing valuable insights into thermoelectric, ferroelectric, and potentially superconducting materials. By achieving a more reliable description of these interactions, the computational framework lays a foundation for future explorations, encouraging both advancements in methodological developments and experimental validations.

In terms of practical implications, this research can significantly influence the design and optimization of materials where anharmonic phonon effects critically impact their macroscopic properties such as thermal conductivity. The reduction of SrTiO$_{3}$'s thermal conductivity, for instance, might advance its application as a thermoelectric material.

Looking forward, there remains scope for extending the theoretical model to incorporate further interactions and intrinsic effects due to cubic anharmonicity. Incorporating a broader range of temperatures and addressing the numerical and methodological challenges related to larger system sizes will be key in enhancing the model's predictive power. Additionally, integrating hybrid functional calculations as suggested by the authors may further improve the quantitative agreement with experimental data.

Overall, this paper marks a considerable step in the pursuit of accurately modeling anharmonic effects in semiconductors and insulators, offering potential insights critical for developing advanced materials in multiple technological domains.