Introduction. The study of the β-InSe crystals is motivated by the potential application of their physical properties in nonlinear optics, solar energy and spintronics. Recently, indium selenide has also attracted considerable attention in view of its use in heterostructures based on the homo- and heterojunctions β-InSe (β-InSe/In4Se3, β-InSe/graphene, InSe/SiC, p-GaSe-n-InSe). In addition to the applied aspects, the β-InSe material is interested from its electronic and dynamical properties related with the layered structure.Purpose. In this work, we present a combined ab initio study of the electronic, structural, dynamical, and elastic properties of the β-InSe layered crystalMethods. Quantum chemical calculations in this work were performed in the framework of density functional theory (DFT) within local approximation for exchange-correlation interaction (LDA) and dispersion correction (DFT-D) methodology.Results. The band structure, the energy dependences of the absorption coefficient for different light polarizations and the dynamic characteristics have been obtained for the β- InSe crystal. We found a direct band gap of about 1.04 eV located at the Г-point in the hexagonal Brillouin zone (Egexp~1.32 eV). The contribution of different bands was analyzed from the partial density of states curves. The phonon dispersion curves and phonon density of states of the material were obtained too. It is shown that the presence of low-frequency optical vibration branches which interact with acoustic vibrations, and LO–TO splitting in the Г–A and Г–M directions in the high-energy region are observed. We carried out the Raman and IR spectra calculations and constructed the vectors of atom displacements corresponding to normal vibration active in these spectra. For the first time calculations of Born effective charges, dielectric constants, and velocities of the sound propagations were carried out for the hexagonal crystal β-InSe.Conclusion. This study reports a detailed investigation on the electronic, the dynamic, the optical and elastic properties for the β-InSe layered crystal using the first-principles method. The calculation provides an excellent description of the electronic band structure and the phonon spectrum. From the calculations of the phonon spectrum, it follows that there is a significant anisotropy for low-frequency acoustic vibration. We have determined the phonon frequencies of the active vibration modes in Raman and IR spectra. Estimates of the Born effective charge, dielectric constants, elastic modules, and ultrasound propagation velocities in the β-InSe crystal show their anisotropy in the direction of strong and weak coupling, and well correlate with the experimental data. 

Представлены первопринципные расчёты электронной структуры и динамических свойств слоистого кристалла β-InSe. Получены зонная структура, энергетические зависимости коэффициента поглощения для разных поляризаций света и вычислены динамические характеристики для данного кристалла. Проанализирована дисперсия фононов и структура спектра комбинационного рассеяния света (КР) и инфракрасного (ИК) спектра. Определена симметрия колебаний, активных в КР и ИК спектрах. Впервые для гексагонального кристалла β-InSe проведены расчёты эффективных зарядов Борна, диэлектрических констант и исследованы упругие свойства.

Представлено першопринципні розрахунки електронної структури та динамічних властивостей шаруватого кристалу β-InSe. Одержано зонну структуру, енергетичні залежності коефіцієнта поглинання для різних поляризацій світла та розраховані динамічні характеристики для даного кристалу. Проаналізована дисперсія фононів та структура спектру комбінаційного розсіювання (КР) і інфрачервоного спектру (ІЧ). Визначена симетрія коливань, активних в КР та ІЧ спектрах. Вперше проведено розрахунки ефективних зарядів Борна, діелектричних констант та досліджені пружні властивості для гексагонального кристалу β-InSe.