First-principles phonon calculations have been widely performed for studying vibrational properties of condensed matter, where the dynamical matrix is commonly constructed via supercell force-constant calculations or the linear response approach. With different manners, a supercell can be introduced in both methods. Unless the supercell is large enough, the interpolated phonon property highly depends on the shape and size of the supercell and the imposed periodicity could give unphysical results that can be easily overlooked. Along this line, we discuss how a traditional method can be used to partition the force constants at the supercell boundary and then propose a more flexible method based on the translational symmetry and interatomic distances. The partition method is also compatible with the mixed-space approach for describing LO–TO splitting. We have applied the proposed partition method to NaCl, PbTiO3, monolayer CrI3, and twisted bilayer graphene, where we show how the method can deliver reasonable results. The proper partition is especially important for studying moderate-size systems with low symmetry, such as two-dimensional materials on substrates, and useful for the implementation of phonon calculations in first-principles packages using atomic basis functions, where symmetry operations are usually not applied owing to the suitability for large-scale calculations.
Tin sulfide (SnS) is one of the promising materials for the applications of optoelectronics and photovoltaics. This study determines the nematic dynamics of photoexcited electrons and phonons in SnS single crystals using polarization-dependent pump–probe spectroscopy at various temperatures. As well as the fast (0.21–1.38 ps) and slow (>5 ps) relaxation processes, a 36–41 GHz coherent acoustic phonon with a sound velocity of 4883 m/s that is generated by the thermoelastic effect is also observed in the transient reflectivity change (Δ R/ R) spectra. Electrons and coherent acoustic phonons show significant in-plane anisotropy from 330 to 430 K due to strong electron–phonon coupling. However, this in-plane anisotropy weakens dramatically in the low-temperature (<330 K) and high-temperature (>430 K) phases. These results add to the knowledge about the anisotropy of electrons and coherent acoustic phonons that give SnS applications in photovoltaic or optoelectronic devices.
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