The Smith hat first drew global attention in 2023 because a single tile could cover an entire surface without ever creating a repeating pattern. Now, the same unusual geometry has produced another surprise: when researchers recreated the pattern at the nanoscale and illuminated it with laser light, it generated optical behavior unlike that of conventional quasicrystals.
Researchers from the Institute of Industrial Science, The University of Tokyo, and collaborating institutions built optical structures based on the Smith hat and investigated how they diffract light. Their findings, published in Nature Communications, reveal that the pattern can produce chiral optical responses, meaning the resulting light patterns have a handedness linked to the structure’s lack of mirror symmetry.
The mathematical foundation comes from the long-standing Einstein problem, which asks whether a single tile shape, or “monotile,” can cover a surface in a non-repeating arrangement. Familiar periodic patterns such as honeycombs and checkerboards repeat regularly. An aperiodic monotile, by contrast, can tile all of space without settling into a repeating pattern.
The Smith hat provided the first solution to that problem in 2023. But solving the mathematical puzzle left another question open: What physical properties might emerge from such an unusual arrangement?
“What is especially fascinating about the hat tile is that, although the resulting pattern appears irregular at first glance, it is actually constructed from the honeycomb lattice,” says lead author Yuto Moritake. “We wanted to see whether this unique shape could also produce any unexpected physical phenomena.”
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