# Making waves

## 20 mar 2024

A team including Oleksandr Gamayun has made the first mechanical metamaterial that transmits topological solitons in just one direction.

Sometimes waves roam alone, rather than in packs. Tsunamis, for example, can travel thousands of miles before making landfall. The meteorological phenomena known as Morning Glory clouds, only observed regularly over Australia’s Gulf of Carpentaria, are sometimes referred to as “the biggest waves on the planet”. Solitary waves of this kind, which move through media without changing their shape, are known as “topological solitons”.

Solitons were first described in detail by the Scottish shipbuilder John Scott Russell in 1834. He was experimenting with canal boat designs on the Union Canal, when he noticed an unusually robust wave rolling down the canal, and followed it on horseback for a couple of miles. Today topological solitons are being explored for possible applications in soft robotics, superconductivity, and quantum computing. String theorists have even speculated that gravitational solitons would bend light into rings and so look very much like black holes from a distance.

Now researchers at the University of Amsterdam and the London Institute for Mathematical Sciences have made the first mechanical metamaterial that reliably transmits topological solitons in just one direction, a key property for avoiding interference in communication applications, for example. They were also able to precisely predict and control the behaviour of these waves using a mathematical model of the material. The research is published in *Nature* today.

“Physicists have long been fascinated by the properties of topological solitons. It’s incredible for me to see these abstract entities in a real material,” says Oleksandr Gamayun, an Arnold Fellow at the London Institute. Gamayun led the work to provide a theoretical description of topological solitons propagating through a sine-Gordon medium, an idealised version of a real material.

His collaborators created the material using a chain of 50 motorised magnetic rotors, linked by elastic bands, and subject to an external magnetic field. Gamayun explains that the new material is able to sustain the solitons because of the subtle interplay between the external magnetic forces, which make the dynamics of the system complex and non-linear, and the material’s “non-reciprocity”, which is its violation of Newton’s third law (for every action there is an equal and opposite reaction). This non-reciprocity forces waves to propagate along the chain in only one direction, like a line of toppling dominoes. And the metamaterial’s design, aligned with Gamayun’s theory, means the waves neither grow nor die out but roll down the length of the material—much as Russell observed almost a hundred years ago.

Dr Gamayun’s Arnold Fellowship is one of five generously funded by leading algorithmic trading company, XTX Markets. They were created in 2022 and named after the Ukrainian-born mathematician Vladimir Arnold.