Self-assembly of isostatic self-dual colloidal crystals

• Main Authors: Lei, Qun-Li, Zheng, Wei, Tang, Feng, Wan, Xiangang, Ni, Ran, Ma, Yu-Qiang
• Other Authors: School of Chemical and Biomedical Engineering
• Format: Article
• Language: English
• Published: 2022
• Subjects: Engineering::Chemical engineering; Energy; Phases
• Online Access: https://hdl.handle.net/10356/153646
• Institution: Nanyang Technological University

Self-dual structures whose dual counterparts are themselves possess unique hidden symmetry, beyond the description of classical spatial symmetry groups. Here we propose a strategy based on a nematic monolayer of attractive half-cylindrical colloids to self-assemble these exotic structures. This system can be seen as a 2D system of semidisks. By using Monte Carlo simulations, we discover two isostatic self-dual crystals, i.e., an unreported crystal with pmg space-group symmetry and the twisted kagome crystal. For the pmg crystal approaching the critical point, we find the double degeneracy of the full phononic spectrum at the self-dual point and the merging of two tilted Weyl nodes into one critically tilted Dirac node. The latter is "accidentally" located on the high-symmetry line. The formation of this unconventional Dirac node is due to the emergence of the critical flatbands at the self-dual point, which are linear combinations of "finite-frequency" floppy modes. These modes can be understood as mechanically coupled self-dual rhombus chains vibrating in some unique uncoupled ways. Our work paves the way for designing and fabricating self-dual materials with exotic mechanical or phononic properties.