Coherent phonons in a $Bi_2Se_3$ film generated by an intense single-cycle THz pulse

We report an observation of coherent phonons of $E_g^1$, $E_u^1$, $A_{1g}^1$, and $E_g^2$ symmetry generated in a single-crystal film of $Bi_2Se_3$ by an intense single-cycle THz pulse. The atomic vibrations reveal themselves through periodic modulation of the refractive index of the film. The largest signal is detected at the frequency of 4.05 THz that corresponds to the $E_g^2$ mode. The generation of $E_g^2$ phonons is interpreted as resonant excitation of the Raman mode by the second harmonic of THz-driven nonlinear $E_u^1$ oscillator, the fundamental frequency of which (2.05 THz) is approximately half that of $E_g^2$. The origin of nonlinearity in this case is cubic lattice anharmonicity, while generation of $E_g^1$ (1.1 THz) and $A_{1g}^1$ (2.25 THz) phonons is a manifestation of quartic anharmonicity enhanced by the occasional combination relations between phonon frequencies in $Bi_2Se_3$.