Anharmonicity of lattice vibrations in Bi$_{2}$Se$_{3}$ single crystals

The temperature dependences of the Raman-active frequencies $E_{g}^{2}$, $A_{1g}^{2}$ in layered Bi$_{2}$Se$_{3}$ single crystals are studied. The contribution of the thermal expansion to a temperature variation in the frequencies is determined. The decay of the anisotropy of the elastic properties in layered Bi$_{2}$Se$_{3}$ single crystals due to strong spin–orbit coupling is shown. The Gruneisen-mode parameters for phonons $E_{g}^{2}$ and $A_{1g}^{2}$ are calculated. Systematic features in the dependences of vibrational frequencies on the atomic masses in layered Bi$_{2}$Te$_{3}$, Bi$_{2}$Se$_{3}$, and Sb$_{2}$Te$_{3}$ single crystals are determined.