One unit cell from one of the two topological insulators.
Photo: L. Brian Stauffer

The universe is loaded with lots of strange symmetries between seemingly dissimilar systems, thanks to similar underlying physics. Take an electrical circuit, a spring, and a swinging pendulum. These simple oscillators might look completely different, but they are governed by the same mathematical equations. Other similarities aren’t so simple—which makes them especially mind-boggling.

Today, separate teams of researchers are announcing another discovery: specially engineered materials, called topological insulators, displaying similar behaviors in very different systems. In these systems, waves can’t travel through the bulk of the medium; they can only exist at the corners. Real-world applications for these systems are likely a ways off, but they have the potential to open a whole new realm of study.

“From a scientific perspective, it opens up a new world,” Gaurav Bahl, University of Illinois engineering professor, told Gizmodo. “We’ve shown that the effect works in two completely different regimes, theirs in acoustics or sound, and ours in microwave frequencies or light, with two different spheres of applications, even though the underlying physics are closely related.”

Physics allows for lots of different materials with strange properties. There are conductors, through which energy can move easily; insulators, which prevent energy from flowing; and semiconductors, which are somewhere in between. But topological insulators are insulators that can conduct only on their surfaces, and systems like these were first discovered in the past few decades. This behavior is topologically protected, meaning that mathematics prevents the edges from losing their wave-trapping behavior, even when the object is deformed.

Physicists have now introduced a new kind of two-dimensional topological insulator, where rather than the edge acting as a conductor, certain kinds of vibrations or waves only exist at the corners. It’s sort of like a square array of empty soda bottles, connected in such a way that if you blow air over all of them equally, only the bottles at the corners make sound. These are the first demonstrations of such an object.


Each team produced their topological insulators in a different way, according to the papers published in Nature. Researchers at ETH Zurich, CalTech, and École Polytechnique Fédérale de Lausanne introduced vibrations with an ultrasound machine to a checkerboard of connected silicon wafers. This led to vibrational resonances at each of the corners.

Meanwhile, the team at the University of Illinois built a similar-looking square array. Each of their unit cells consisted of specially fabricated copper circuits called resonators. These resonators absorb specific frequencies of microwave radiation. When they were connected and received microwave radiation, the corners absorbed at a characteristic frequency that the rest of the units did not. When they tuned the system to effectively detach the bottom row from the rest of the grid, the next highest row’s corners did the absorbing, showing the topological effects.

“The resonators are coupled in a special way that emulates how atoms would be coupled together in a quadrupole topological insulator,” explained Kitt Peterson, lead author of one of the two papers published in Nature and an electrical engineering graduate student at the University of Illinois.


Basically, this behavior in topological insulators arises from the collective structure of the system, called its quadrupole moment. If each topological insulator were a square array of atoms, as opposed to specially fabricated systems, it would be as if extra charge accumulated on the corners. A third team of European scientists created a different specialized circuit and published their result on the arXiv.

And physicists are excited.

“The two papers ... are in my opinion both extremely convincing,” Stephanie Law, University of Delaware materials science professor, told Gizmodo. Such different systems demonstrating a behavior so similar shows something profound. “I think that’s really amazing. You have these two papers showing the same effect in two completely different systems,” she said. “It really illustrates how general this concept is.”


What do you actually do with materials like this? It’s too early to say, and they’re still really hard to make. Both groups told Gizmodo they’d be looking to miniaturize their systems—right now, they’re tabletop sized. Perhaps they could be used in communications and computing. As I joked with Law, the person who discovered the semiconductor probably didn’t know they’d be crucial for building iPhones.

There’s work left to be done, and potentially more interesting things to find. “Stacking the type of systems we have into the third dimension, you might have all kinds of interesting physics similar to what we’ve seen but one dimension higher,” Sebastian Huber, professor in Condensed Matter and metamaterials from ETH Zurich, told Gizmodo. Maybe the behavior would exist at the edges of a cube, rather than the corners of a square. Maybe there are even higher-order topological insulators caused by “octopoles,” where the waves only propagate at the corners of a cube.

And discoveries are always nice. Said Huber: “We’re excited by doing new stuff that hasn’t been observed.”


[Nature 1, 2, arXiv]