One of the basic properties of spatial crystals is that they form when a system drops to its lowest possible energy state. They are not the result of adding energy to a system, but of taking it away. All of it.
Another basic property is that when these objects reach their lowest energy configuration, their symmetry breaks down. Instead of being the same in all directions, like the laws of physics, these objects become the same in only a few directions. It is this symmetry-breaking and the periodic structure it produces that defines crystals.
Wilczek and Shapere persuasively argued that there’s no reason why similar periodic structures couldn’t exist in time. And they said that finding them would give physicists a new way to study the process of symmetry-breaking and the laws of physics behind it.
Researchers 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.
The idea of a permanently rotating ring might have uncomfortable parallels with a perpetual motion device. But a space-time crystal does not violate any laws of physics. That’s because it exists in its lowest energy state and so cannot do work–energy cannot be extracted from this system even though it is moving.
That’s more than a mere curiosity. One reason why space-time crystals are interesting is that their periodicity in time makes them natural clocks. So there should be plenty of people with more than a passing interesting in making one.
And that should be sooner rather than later. Tongcang and co’s space-time crystal ought to be possible to make now using state of the art ion traps.
Abstract- Great progresses have been made in exploring exciting physics of low dimensional materials in last few decades. Important examples include the discovering and synthesizing of fullerenes (zerodimensional,0D) , carbon nanotubes (1D)  and graphene (2D) . A fundamental question is whether we can create materials with dimensions higher than that of conventional 3D crystals, for example, a 4D crystal that has periodic structures in both space and time. Here we propose a space-time crystal of trapped ions and a method to realize it experimentally by confining ions in a ring-shaped trapping potential with a static magnetic field. The ions spontaneously form a spatial ring crystal due to Coulomb repulsion. This ion crystal can rotate persistently at the lowest quantum energy state in magnetic fields with fractional fluxes. The persistent rotation of trapped ions produces the temporal order, leading to the formation of a space-time crystal. We show that these space-time crystals are robust for direct experimental observation. The proposed space-time crystals of trapped ions provide a new dimension for exploring many-body physics and emerging properties of matter.