Emergence of an enslaved phononic bandgap in a non-equilibrium pseudo-crystal.

Material systems that reside far from thermodynamic equilibrium have the potential to exhibit dynamic properties and behaviours resembling those of living organisms. Here we realize a non-equilibrium material characterized by a bandgap whose edge is enslaved to the wavelength of an external coherent drive. The structure dynamically self-assembles into an unconventional pseudo-crystal geometry that equally distributes momentum across elements. The emergent bandgap is bestowed with lifelike properties, such as the ability to self-heal to perturbations and adapt to sudden changes in the drive. We derive an exact analytical solution for both the spatial organization and the bandgap features, revealing the mechanism for enslavement. This work presents a framework for conceiving lifelike non-equilibrium materials and emphasizes the potential for the dynamic imprinting of material properties through external degrees of freedom.