Hyperuniform Structures Formed by Shearing Colloidal Suspensions*

In periodically sheared suspensions there is a dynamical phase transition characterized by a critical strain amplitude between an absorbing state where particle trajectories are reversible (all particles return to their same position cyclically) and an active state where trajectories are chaotic and diffusive. A simple toy model called Random Organization, RO, qualitatively reproduces the dynamical features of this transition. In RO overlapping particless are considered active and every cycle each active particle is given a random displacement of a maximum size ε. Random Organization and other absorbing state models exhibit hyperuniformity, a strong suppression of density fluctuations on long length-scales quantified by a structure factor S(q) that approaches 0 as a power law in q at criticality. Here we show experimentally that the particles in periodically sheared suspensions organize into structures with anisotropic short-range order but isotropic, long-range hyperuniform order when oscillatory shear amplitudes approach the critical strain. Further, a modification of the model, Biased Random Organization, where some fraction of the displacements of active particles are repulsive, remains in the same universality class, has at it's highest density, its critical endpoint as ε → 0, and reproduces the elusive random close packed state which hence is also hyperuniform.