Dynamical breaking of inversion symmetry, strong second harmonic generation, and ferroelectricity with nonlinear phonons

We show how crystalline inversion symmetry can be dynamically broken by optical phonons with generic, hardening Kerr-like non-linearities. The symmetry-broken state is reached through a parametric instability that can be accessed by driving close to half the phonon resonance. After the onset of the instability, the system settles to a steady state with inversion-symmetry breaking phonon trajectories and strong second harmonic generation. The time averaged positions of the atoms are displaced relative to equilibrium, resulting in a ferroelectric rectification of the driving signal.