How to Build A Space-Time Crystal: These guys say they know how to create an object in its lowest energy state that shows periodic structure both in space and time--a space-time crystal.
Their idea is remarkably simple. Their space-time crystal consists of a cloud of beryllium ions trapped in an circular electromagnetic field. The ions naturally repel each other and so spontaneously form a circle. That's a type of spatial ionic crystal, something physicists have played with for years.
However, if Wilczek and Shapere are right, this ring of ions ought to rotate, even when cooled almost to absolute zero. Such a rotating ring is periodic both in space and in time and so becomes a space-time crystal.