Characteristics of Raman spectra of 2$H$-$\alpha$-In$_2$Se$_3$ layered crystals of different thicknesses

The results of studies of the vibrational properties of layered $\alpha$-In$_2$Se$_3$ crystals when the number of constituent layers is varied are presented. The joint analysis of Raman spectroscopy and atomic force microscopy data, followed by theoretical group analysis of vibrational modes, has allowed us to establish the patterns of changes in the parameters of spectral lines in the range of high and ultra-low ($\omega<$ 50 cm$^{-1}$) frequencies. It is shown for the first time that the position of the high-frequency line $A_1$(3) ($\omega\sim$ 200 cm$^{-1}$) can be used to estimate the thickness of $\alpha$-In$_2$Se$_3$ in the range of seven to several tens of layers.