Spatiotemporal order and parametric instabilities from first-principles

Shaping crystal structure with light is an enduring goal of physics and materials engineering. Here we present calculations in candidate materials selected by symmetry that allow light-induced spatiotemporal parametric instabilities. We demonstrate a theoretical framework that includes a complete symmetry analysis of phonon modes that contribute to parametric instabilities across all non-centrosymmetric point groups, a detailed survey of the materials landscape and finally the computation of nonlinear couplings from first principles. We then showcase detailed results for chiral crystals, ferroelectrics, and layered van der Waals materials. Our results pave the way towards realizing designer time-crystalline order in quantum materials, detectable with time-resolved diffractive probes.