Tetratic phase in 2D crystals of squares

Abstract

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.