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The spontaneous breaking of symmetries is a widespread phenomenon in physics.When time translational symmetry is spontaneously broken, an exoticnonequilibrium state of matter in which the same structures repeat themselvesin time can arise. This state, known as "time crystal", attracted a lot ofinterest recently. Another relatively new research area deals with activematter. Materials consisting of colloidal particles that consume energy fromtheir environment and propel themselves forward can exhibit intriguingproperties like superfluidity that were previously known only fromquantum-mechanical systems. Here, we bring together these - at first glancecompletely different - research fields by showing that self-propelled colloidalparticles can form classical continuous time crystals. We present a statediagram showing where this new state of matter arises. Furthermore, weinvestigate its tempomechanical properties and present a temporal stress-straindiagram showing parallels to conventional materials science but also remarkablenew properties that do not have a counterpart in common materials.

A colloidal time crystal and its tempomechanical properties