Self-Assembly of Isostatic Self-Dual Colloidal Crystals

Abstract

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.

Systematic generation of Hamiltonian families with dualities

“…Similar notions of dualities were suggested in systems ranging from self-assembled systems [10] to quantum rotors [11]. Rich consequences arise when a duality is combined with other constraints such as symmetries or conservation laws, ranging from degeneracies in the band structure [12][13][14] and topological states [15,16] to symmetries in the phonon response [17] and constraints on the stiffness tensor of an elastic medium [18].…”

Topological Metamaterials

“…Additionally, classical platforms possess unique properties beyond their condensed matter counterparts, benefiting interdisciplinary fields. Notably, long-range coupling, recently uncovered dualities, , fragile topology, topological quantum chemistry in photonics, and non-Abelian topological effects ,− can all pave the way for exciting topological phenomena for light propagation, sound, and mechanical vibrations in chemistry. Researchers are eager to harness this relatively new field in photonics, phononics, and interdisciplinary fields, for instance, by designing and fabricating disorder-immune components for high-speed information transfer and processing in on-chip designs integrated with optical or acousto-optic elements.…”

Computer simulations of self-assembly of anisotropic colloids

“…They varied the Janus balance (fraction of hydrophobic surface of the particle) and particle concentration and obtained onion phases, micellar, lamellar structures. Lei et al reported self-assembly of halfdiscs in 2D using depletion attraction between the curved sides [99]. They predicted a hexagonal lattice at high densities and gas phase at low densities.…”