Time Crystals in their ground state are moving through time, not space, breaking quantum time translation symmetry.
more detail, sorta layman
time-crystals-might-exist- after-all-and-they-could- break-the-symmetry-of-space- and-time
“The significance of our work is two-fold: on one hand, it demonstrates that time-translation symmetry is not immune to being spontaneously broken,” said coauthor Bela Bauer, a researcher at Microsoft Station Q. “On the other hand, it deepens our understanding that non-equilibrium systems can host many interesting states of matter that cannot exist in equilibrium systems.” Read more
and some more:
rambling nonsense has some fine comments about it here:
science/comments/5289p0/time_ crystals_objects_whose_ structure_would/d7iapdn?st= it1y6yfa&sh=5e77fe0e