Gardner Phenomenology in Minimally Polydisperse Crystalline Systems

We study the structure and dynamics of crystals of minimally polydisperse hard spheres at high pressures. Structurally, they exhibit a power-law scaling in their probability distribution of weak forces and small interparticle gaps as well as a flat density of vibrational states. Dynamically, they display anomalous aging beyond a characteristic pressure. Although essentially crystalline, these solids thus display features reminiscent of the Gardner phase observed in certain amorphous solids. Because preparing these materials is fast and facile, they are ideal for testing a theory of amorphous materials. They are also amenable to experimental realizations in commercially-available particulate systems.