Self-organized chiral colloidal crystals of Brownian square crosses.

We study aqueous Brownian dispersions of microscale, hard, monodisperse platelets, shaped as achiral square crosses, in two dimensions (2D). When slowly concentrated while experiencing thermal excitations, the crosses self-organize into fluctuating 2D colloidal crystals. As the particle area fraction φA is raised, an achiral rhombic crystal phase forms at φA ≈ 0.52. Above φA ≈ 0.56, the rhombic crystal gives way to a square crystal phase that exhibits long-range chiral symmetry breaking (CSB) via a crystal-crystal phase transition; the observed chirality in a particular square crystallite has either a positive or a negative enantiomeric sense. By contrast to triangles and rhombs, which exhibit weak CSB as a result of total entropy maximization, square crosses display robust long-range CSB that is primarily dictated by how they tile space at high densities. We measure the thermal distribution of orientation angles γ of the crosses' arms relative to the diagonal bisector of the local square crystal lattice as a function of φA, and the average measured γ (φA) agrees with a re-scaled model involving efficient packing of rotated cross shapes. Our findings imply that a variety of hard achiral shapes can be designed to form equilibrium chiral phases by considering their tiling at high densities.