Dynamical Breaking of Inversion Symmetry, Strong Second Harmonic Generation, and Nonequilibrium Ferroelectricity with Nonlinear Phonons.

We show how crystalline inversion symmetry can be dynamically broken by optical phonons with generic, hardening Kerr-like nonlinearities. The symmetry-broken state is reached through a parametric instability that can be accessed by driving close to half the phonon frequency. The system then 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. For circularly polarized phonons, complex Lissajous-like trajectories, resulting in structured magnetic fields within a unit cell, can be achieved.