Tetratic phase in 2D crystals of squares

Melting in two-dimensional (2D) systems is described by the celebrated Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, which explains how the unbinding of two types of topological defects destroys translational and orientational order at distinct temperatures. The intermediate hexatic phase, a fluid with six-fold quasi-long-ranged orientational order, has been observed in 2D colloidal monolayers of isotropic particles. In this study, we investigate the melting of a quadratic crystal with four-fold symmetry, composed of square particles of approximately 4 × 4 μm in size. These anisotropic particles were fabricated from photoresist using 3D nanoprinting. In an aqueous solution, the particles sediment onto a cover slide, forming a monolayer. The adjustable curvature of the cover slide precisely controls the monolayer density. At low densities, the particles exhibit free diffusion, forming a 2D fluid, while at high densities, they assemble into a quadratic crystal. Using a four-fold bond-order correlation function, we identify the tetratic phase with quasi-long ranged orientational order in close analogy to the hexatic phase in systems with six-fold symmetry.