An active colloidal system showing parallels to a time crystal

Abstract

The spontaneous breaking of symmetries is a widespread phenomenon in physics. When time translational symmetry is spontaneously broken, an exotic nonequilibrium state of matter in which the same structures repeat themselves in time can arise. This state, known as ‘time crystal’, attracted a lot of interest recently. Another relatively new research area deals with active matter. Materials consisting of colloidal particles that consume energy from their environment and propel themselves forward can exhibit intriguing properties like superfluidity that were previously known only from quantum-mechanical systems. Here, we bring together these—at first glance completely different—research fields by showing that self-propelled colloidal particles show parallels to classical continuous time crystals. We present a state diagram showing where this state of matter arises. Furthermore, we investigate its properties and analyze the interactions between the particles leading to the dynamics.