Traditional crystals are composed of extremely orderly, symmetrically arranged repeating patterns of atoms that don’t move. Recently, however, a team of physicists has proposed a type of crystal that gets its symmetry from the elegant movement of its components, like a swarm of satellites in space.
Thinking about the space-based gravitational wave detector eLISA led Latham Boyle, a physicist at the Perimeter Institute for Theoretical Physics in Ontario, to theorize a new spin on crystals. The eLISA mission, which will launch in the late 2020s, is made up of three satellites. Once in orbit, they will be able to catch harder-to-detect waves than their Earthbound equivalent, LIGO, which successfully detected gravitational waves last September as announced on February 11, 2016. If a gravitational wave passes through, the distances between the satellites will change very slightly.
Boyle wanted to know what would happen if the number of satellites changed. “The fact that eLISA only has three satellites means they always lie in a plane,” Boyle explains, rather than a three dimensional swath of space. This does not impede eLISA’s ability to pick up gravitational waves but means it needs time to determine the source and detailed characteristics of a wave. It can get a good picture of a continuous, long-lasting signal as it moves through space and builds up multiple detections of the same signal but it lacks the time to do the same for short-lived ones. Dreaming of a “pie-in-the-sky,” next-generation space-based detector that could instantly characterize these quick signals, Boyle wondered what would happen if the detector had four satellites instead of three and what would be the most stable four-object orbit. “Originally we were thinking about this gravitational-wave problem but that led to this question of what is the most symmetrical four-satellite object,” Boyle explains. Once they discovered the dynamic orbit, they shifted gears again to look for ways that their interesting orbit could be generalized. “We first began by trying to find more general satellite orbits but then we quickly began to think this idea seems more general than just about satellites. Why couldn’t the atoms or electrons in a crystal do analogous dances?”
In a static arrangement, the most orderly arrangement of four objects is a triangular pyramid. The dynamically symmetric order for the satellites Boyle’s team ultimately found also uses this tetrahedron shape but adds in time and motion: Each object revolves around a central point, like satellites about the sun, in an orbit parallel to one face of a regular tetrahedron. The four satellites appear to make a square six times per orbit. In such a system, if observers could stand on each orbiting component, they would all have an identical view.“What the folks have done with the choreographic crystals is think about the components in your lattices having some kind of dynamical behavior,” says Jim Crutchfield, director of the Complexity Sciences Center at the University of California, Davis. “They’re thinking about exactly periodic behavior. What you get is this very beautiful interaction.”
Crutchfield is a fan of challenging the crystalline status quo, and the notion of crystals that take their symmetry not from their structure but their motion fits in with the wider sphere of unconventional crystals he studies. Other key members of this growing group of crystals include quasicrystals, which were formally discovered by Nobel chemistry laureate Dan Shechtman in 1982 and exhibit forbidden symmetries as well as lack the repeating uniform patterns found in normal crystals, and spacetime crystals, whose particles move periodically and return to their initial state.
This animation shows the most symmetric orbit for four satellites. A still image of it at any one point would likely look disorganized, but while in motion its symmetry can be seen.
Similar to Boyle’s choreographic crystals, spacetime crystals include a time and motion aspect. The similarity might indicate a relationship between the two types of crystals. “If these [choreographic crystals] exist—and that’s a big if—it would describe the symmetry of the ground state of not regular crystals but these time crystals,” Boyle suspects.
Frank Wilczek, a professor of physics at Massachusetts Institute of Technology who first proposed spacetime crystals in 2012, thinks Boyle’s hypothetical link between the exotic crystal types is a strong one. He hopes to see more research into how these choreographic crystals might occur, particularly dealing with how they are put into motion in the first place. “[The authors are] classifying interesting patterns that are mathematically consistent that might arise, without specifying what the physical realizations might be and whether it requires driving input or not,” Wilczek says. “The general question of finding patterns and classifying the possibilities is really interesting, and the question of exactly what it takes to make such systems is also exciting.”
There is precedent for theorized materials to be realized in the lab or discovered in nature, so detecting or inventing choreographic crystals is not impossible. Whereas the applications of these strange crystals is unknown, their potential is on researchers’ minds. “Those of us playing around in this nouveau-crystal arena, we’re all looking for the physical impact, the material property,” Crutchfield says.
Wilczek takes a more theoretical approach. “There might be a practical benefit in the long run, but for sure it’s fun and has nice mathematics,” he says. What those practical applications would be are unknown, but the potential is exciting. Classifying these crystals is necessary to explore their potential, to hunt for examples that occur in nature or to try to develop lab-made ones. From there, how the introduction of dynamic motion changes things such as thermal properties or how electrons move through the material could be determined.
For the time being their application is less important than the fact that exotic crystals are being investigated in the first place, in Crutchfield’s opinion. “Nature’s trying to talk to us, we’re just not listening,” he says. “What they have in the choreographed crystals is a dynamical version of the push to break out of this idealized crystal structure.”