Gyromorphs: a new class of functional disordered materials

Both periodic and quasiperiodic systems are characterized by extensive peaks in their structure factors, the most intense of which form regular shapes – in two dimensions, square lattices have a square of high peaks, triangular lattices a hexagon, and quasicrystals have a higher order polygon. Disordered structures, on the other hand, typically only have broad, isotropic Fourier-space features. It then seems safe to assume that polygons of high peaks are a specific feature of (quasi)periodicity.

In this talk, I show that, contrary to established wisdom, disordered structures with a ring of regularly spaced extensive peaks exist. I show that these structures, which we call gyromorphs, achieve quasi-long-range rotational and translational orders in spite of isotropic neighborhoods akin to those observed in liquids. These seemingly contradictory features set them apart from any other known structures. In particular, even at high orders of rotational symmetry, gyromorphs achieve peaks higher, and better resolved, than finite quasicrystals.

These high peaks make gyromorphs particularly well suited as photonic bandgap materials, as shown by simple simulations.

Finally, I show that gyromorphs may be generalized to 3d structures, or structures with several rings of peaks, paving the way for photonic applications.