Physicists build crystal from 13-sided 'einstein' tile, bending light into pinwheel pattern
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University of Tokyo physicists have fabricated a photonic crystal using the 13-sided 'hat' tile, a shape that tiles a plane without repeating. The crystal, described in Nature Communications, scatters laser light into a swirling pinwheel pattern that changes with the light's spin. The nanoscale structure was made by etching hundreds of thousands of 100-nanometer-radius holes into silicon nitride.
The Hat Tile's Origin
Mathematicians long sought a single shape—an 'einstein'—capable of covering a surface with an aperiodic pattern. In the 1970s, Roger Penrose showed that two shapes could achieve this, but the single-shape solution remained elusive. In 2023, geometry enthusiast David Smith discovered a 13-sided polygon, dubbed the 'hat' tile, that finally solved the einstein problem. The tile can tile infinitely with no repeating patches, a property called aperiodic order.
Crystal Fabrication
Yuto Moritake, an experimental physicist at the University of Tokyo, encountered the hat tile in a 2024 popular science book and decided to integrate it into a photonic crystal. Using electron beam lithography and etching, his team carved hundreds of thousands of holes, each 100 nanometers in radius, into a silicon nitride film. The holes were arranged according to the hat tile's aperiodic pattern, covering a chip about half a millimeter wide. Silicon nitride is widely used in computer chips, providing a durable substrate.
Light-Scattering Results
When the team directed a laser at the chip, light diffracted into a pinwheel-shaped pattern of bright spots, known as Bragg peaks. The spots remained fixed regardless of the laser's position on the crystal, indicating long-range aperiodic order. The diffraction pattern also responded to the circular polarization of the laser, with a clockwise-spinning beam producing a different pattern than a counterclockwise one. Moritake first captured the phenomenon using a smartphone's long-exposure mode before detailed camera measurements.
What's Next
Moritake’s group is now investigating whether the structure can be optimized for applications such as beam steering or optical sensing. It remains unclear if the aperiodic photonic crystal can outperform conventional periodic crystals in practical devices.
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Physicists build crystal from 13-sided 'einstein' tile, bending light into pinwheel pattern
