Photonic Band Gaps in Colloidal Crystals of Chiral Hedgehogs

Colloidal crystals are desirable for photonic bandgaps, that can be tuned by the change in periodic arrangement of particles. While spherical particles are a trivial shape to crystallize, their monodispersity determines the long-range order that is achievable [¹]. Here we report the formation of colloidal crystals from spherically shaped chiral microparticles of gold-cysteine complexes [²]. These microparticles are self-assembled from twisted spikes whose length, width and twist angle can be controlled by physical-chemical parameters such as enantiomeric excess, temperature, and charge screening. Using a mixture of L- and D-cysteine we self-assemble chiral hedgehogs of diameters 1-10 µm, at temperatures of 30-90^o C. Machine vision algorithms reveal that 1 µm diameter hedgehogs show higher hexatic order parameter [³] as compared to larger sized hedgehogs. Using two-phase self-assembly we deposit these crystals over 1 cm x 1 cm region through controlled evaporation and study their photonic properties. Inherent chirality of hedgehogs imparts an added dimension to photonic bandgaps by their differential interaction with left- vs right-polarized electromagnetic wave. We evaluate these differences through finite element modeling and generate a band diagram for chiral colloidal crystals.<br/><br/>1. Manoharan, V. N., Elsesser, M. T. & Pine, D. J. Dense packing and symmetry in small clusters of microspheres. <i>Science (1979)</i> <b>301</b>, 483–487 (2003).<br/>2. Jiang, W. <i>et al.</i> Emergence of complexity in hierarchically organized chiral particles. <i>Science (1979)</i> <b>368</b>, 642–648 (2020).<br/>3. Bernard, E. P. & Krauth, W. Two-step melting in two dimensions: First-order liquid-hexatic transition. <i>Physical Review Letters</i> <b>107</b>, 155704 (2011).