Tokyo Researchers Find Chiral Light Effects in Nanoscale 'Einstein Tile' Patterns

Researchers at the Institute of Industrial Science, The University of Tokyo, and collaborating institutions have built nanoscale optical structures based on the Smith hat tile — the 2023 solution to the mathematical Einstein problem — and reported in Nature Communications that it produces an unusual chiral, or ‘handed,’ light-diffraction effect, meaning the light pattern is not identical to its mirror image.

The Einstein problem asks whether a single tile shape, or ‘aperiodic monotile,’ can cover a surface without ever repeating, unlike periodic patterns such as honeycombs or checkerboards. “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,” said lead author Yuto Moritake. “We wanted to see whether this unique shape could also produce any unexpected physical phenomena.”

To find out, the team used electron-beam lithography to fabricate nanoscale Smith hat patterns on silicon nitride films, then illuminated them with laser light and studied the resulting diffraction — the pattern light forms after interacting with a material. Instead of behavior typical of conventional quasicrystals, the structures produced distinctive pinwheel-like diffraction patterns. “We found that the diffraction patterns themselves become chiral because the structure lacks mirror symmetry,” said senior author Masaya Notomi. “This kind of optical response is fundamentally different from that observed in conventional quasicrystalline materials.”

The effect was not fixed: changing the direction or polarization of the incoming light changed the diffraction pattern, and creating mirror-image versions of the structures reversed the optical behavior accordingly, revealing a symmetry-controlled response. “These results open a new direction of research on the fusion of quasiperiodic order and chirality,” Moritake said. Researchers hope monotile-inspired structures could eventually help manipulate light, control polarization, and enable new optical devices.

The study, titled ‘Chiral diffraction from aperiodic monotile structure,’ was published in Nature Communications on 29 July 2026, and authored by Moritake, Masato Takiguchi, Takuma Aihara and Notomi.