Hyperuniformity and Photonic Properties in Solids with Bond-Orientational Order

Abstract

Recent studies suggest that hyperuniformity, the anomalous suppression of density fluctuations on large scales, may be a necessary condition for various transport properties in solids. Advances in materials science, nanotechnology, and atomic physics will soon allow for the construction of solids that are impossible by thermodynamic processes alone. Adopting this broader view of the landscape of possible structures, one class of solids that offers immense variety is those with bond-orientational order. Beyond perfect quasicrystals, the hyperuniformity and transport properties of such systems have yet to be explored. We introduce HyperBOO (Hyperuniform Bond-Orientational Ordered) structures as a promising new class of solids, both for exploring the connection between hyperuniformity and transport, and as interesting systems in themselves that could posses novel properties desirable in future technologies. In this work, we focus on the photonic properties of these systems. We first characterize the hyperuniformity of a selection of BOO structures, and identify several of them as HyperBOO. We modify the prescription for generating periodic approximants of perfect quasicrystals to accommodate a much larger variety of BOO tilings, allowing us to study the photonic band gaps of these systems. We apply this procedure to a selection of BOO structures for which the hyperuniformity was characterized earlier. These tests are inconclusive in addressing whether HyperBOO structures outperform non-hyperuniform BOO systems in terms of the widths of their photonic band gaps. Future research will be aimed at constraining the photonic band gaps of these systems.