Features of coherent phonons of the strong topological insulator Bi$_2$Te$_3$

Femtosecond laser pulses have been used to generate and detect fully symmetric ($A_{1g}$) and doubly degenerate ($E_g$) coherent phonons in the topological insulator Bi$_2$Te$_3$. The isotropic detection of the low-symmetry $E_g$ modes has been obtained in the case of excitation in the near infrared range ($\lambda=1300$ nm) and these modes have not been observed in the case of excitation with $\lambda=830$ nm. The comparison of the amplitudes and initial phases of the coherent phonons indicates that the mechanisms of the excitation of fully symmetric ($A_{1g}$) and doubly degenerate ($E_g$) modes in the topological insulator are different.