Back in 2012, Frank Wilczek proposed the idea of time crystals, here and here, for classical and quantum versions, respectively. The original idea in a time crystal is that a system with many dynamical degrees of freedom, can in its ground state spontaneously break the smooth time translation symmetry that we are familiar with. Just as a conventional spatial crystal would have a certain pattern of, e.g., density that repeats periodically in space, a time crystal would spontaneously repeat its motion periodically in time. For example, imagine a system that, somehow while in its ground state, rotates at a constant rate (as described in this viewpoint article). In quantum mechanics involving charged particles, it's actually easier to think about this in some ways. [As I wrote about back in the ancient past, the Aharonov-Bohm phase implies that you can have electrons producing persistent current loops in the ground state in metals.]
The "ground state" part of this was not without controversy. There were proofs that this kind of spontaneous periodic groundstate motion is impossible in classical systems. There were proofs that this is also a challenge in quantum systems. [Regarding persistent currents, this gets into a definitional argument about what is a true time crystal.]
Now people have turned to the idea that one can have (with proper formulation of the definitions) time crystals in driven systems. Perhaps it is not surprising that driving a system periodically can result in periodic response at integer multiples of the driving period, but there is more to it than that. Achieving some kind of steady-state with spontaneous time periodicity and a lack of runaway heating due to many-body interacting physics is pretty restrictive. A good write-up of this is here. A theoretical proposal for how to do this is here, and the experiments that claim to demonstrate this successfully are here and here. This is another example of how physicists are increasingly interested in understanding and classifying the responses of quantum systems driven out of equilibrium (see here and here).
The "ground state" part of this was not without controversy. There were proofs that this kind of spontaneous periodic groundstate motion is impossible in classical systems. There were proofs that this is also a challenge in quantum systems. [Regarding persistent currents, this gets into a definitional argument about what is a true time crystal.]
Now people have turned to the idea that one can have (with proper formulation of the definitions) time crystals in driven systems. Perhaps it is not surprising that driving a system periodically can result in periodic response at integer multiples of the driving period, but there is more to it than that. Achieving some kind of steady-state with spontaneous time periodicity and a lack of runaway heating due to many-body interacting physics is pretty restrictive. A good write-up of this is here. A theoretical proposal for how to do this is here, and the experiments that claim to demonstrate this successfully are here and here. This is another example of how physicists are increasingly interested in understanding and classifying the responses of quantum systems driven out of equilibrium (see here and here).