Space-time crystals from particle-like topological solitons

Abstract: Time crystals are unexpected states of matter that spontaneously break time translation symmetry either in a discrete or continuous manner. However, spatially-mesoscale space-time crystals that break both the space and time symmetries have not been reported. Here we report a continuous space-time crystal in a nematic liquid crystal driven by ambient-power, constant-intensity unstructured light. Our numerically constructed 4-dimensional configurations exhibit good agreement with these experimental findings. While meeting the established criteria to identify time-crystalline order, both experiments and computer simulations reveal a space-time crystallization phase formed by particle-like topological solitons. The robustness against temporal perturbations and spatiotemporal dislocations shows the stability and rigidity of the studied space-time crystals, which relates to their locally topological nature and many-body interactions between emergent spontaneously-twisted, particle-like solitonic building blocks. Their potential technological utility includes optical devices, photonic space-time crystal generators, telecommunications, and anti-counterfeiting designs, among others.