New type of symmetry discovered, hidden in artificial materials

Autodual symmetries emerge at critical points, causing two completely different materials to conduct sound in the same way.

It is not every day that you discover a new type of symmetry in nature.
Even less discover symmetries hidden in man-made artificial materials.
And the discovery has numerous immediate practical applications.

A trio of researchers from the University of Chicago, USA, discovered a symmetry hidden inside the solids when using sound waves to study the interior of the materials. They used Lego blocks to build regular structures and assess how they react to sound.

What they found is that completely different structures can produce the same sound - something like hitting a green watermelon and a ripe watermelon and hearing the same sound.

"What excited us was the fact that we cannot explain our findings using existing concepts, such as spatial symmetries," said Professor Vincenzo Vitelli, recalling that physicists have used these concepts for decades to describe and predict the properties of an object with based on their spatial symmetries.

The new explanation that has emerged is what the researchers call "duality", a hidden symmetry associating apparently unrelated parts of the solid.

"We observed that pairs of distinct configurations along the mechanism have the same vibrational spectrum and related elastic modules. We demonstrated that these intriguing properties arise from a duality between pairs of configurations on both sides of a critical mechanical point," wrote the team. In other words, it is a self-duality, which emerges when a duality becomes recurrent in a periodic material.

In the past few years, there has been an explosion of interest in a field called metamaterials. These are artificial structures engineered to have characteristics not normally expected in nature. For example, much thought has gone into realizing an "invisibility cloak" using composite materials that bend incoming light around them by virtue of their internal geometry.

Fruchart and Vitelli imagined using this approach to take a particle such as a phonon—essentially a particle of heat—and give it properties that it doesn't usually have.

The discovery of this duality promises to have a great impact on the design of metamaterials , allowing to design artificial materials that have specific properties.

Most metamaterials have been designed to handle light, but this new symmetry paves the way for the design of artificial materials that manipulate sound - phonons, which are "particles of heat", rather than photons, particles of light.

Electrons have a property called "spin", which is used as the basis for some of the latest high-tech electronics. Phonons, in turn, do not have an intrinsic spin, but if it is possible to shape the structure of materials, it is possible to give phonons a "pseudo-spin". Vitelli and his colleagues called this concept "mechanical spintronics".

This would allow us to use these materials in phononic devices - similar to electronics, but with different skills, enabling phononics, or "heat electronics".

"Our approach also applies to other waves, not just phonons - for example, waves of light and matter," said researcher Michel Fruchart.


Article: Dualities and non-Abelian mechanics

Authors: Michel Fruchart, Yujie Zhou, Vincenzo Vitelli

Magazine: Nature

Vol .: 577, pages 636-640

DOI: 10.1038 / s41586-020-1932-6

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