Phonon-driven ultrafast symmetry lowering in a Bi$_2$Se$_3$ crystal
Selective excitation of coherent high-amplitude vibrations of atoms in a solid can induce exotic nonequilibrium states, in which the character of interactions between electronic, magnetic and lattice degrees of freedom is considerably altered and the underlying symmetries are broken. Here we use intense single-cycle terahertz pulses to drive coherently the dipole-active $E_u^1$ phonon mode of a Bi$_2$Se$_3$ crystal. As a result, several Raman-active modes are simultaneously excited in a nonlinear process, while one of them, having the $E_g^2$ symmetry, experiences dynamical splitting during the first two picoseconds after excitation. The corresponding angular scattering pattern is modified indicating coexistence of two phonon modes characteristic of a nonequilibrium state with a lower crystal symmetry. We observe also a short-lived frequency splitting of the original $E_g^2$ mode that immediately after excitation amounts to $\sim 25\%$ of the unperturbed value. This transient state relaxes with a characteristic time of $\sim$ 1 ps, that is close to the decay time of the squared amplitude of the resonantly excited infrared-active $E_u^1$ mode. We discuss possible mechanisms of the dynamical splitting: nonlinear lattice deformation caused by the intense $E_u^1$ vibrations and excitation of anisotropic electronic distribution due to nonlinear electron-phonon interaction. Our data also contain an evidence in favor of the sum-frequency Raman mechanism of generation of the coherent $E_g^2$ phonons in Bi$_2$Se$_3$ excited by terahertz pulses.