Hyperuniform structures formed by shearing colloidal suspensions

In periodically sheared suspensions there is a dynamical phase transition, characterized by a critical strain amplitude ${\ensuremath{\gamma}}_{c}$, between an absorbing state where particle trajectories are reversible and an active state where trajectories are chaotic and diffusive. Repulsive nonhydrodynamic interactions between ``colliding'' particles' surfaces have been proposed as a source of this broken time reversal symmetry. A simple toy model called random organization qualitatively reproduces the dynamical features of this transition. Random organization and other absorbing state models exhibit hyperuniformity, a strong suppression of density fluctuations on long length scales quantified by a structure factor $S(q\ensuremath{\rightarrow}0)\ensuremath{\sim}{q}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}g0$, 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 ${\ensuremath{\gamma}}_{c}$.