Quasicrystalline Order in Soft Matter Systems

Since their groundbreaking discovery in Al-Mn alloys, quasicrystals have attracted considerable interest due to their unique structural characteristics and promising applications. These structures challenge traditional crystallographic concepts by exhibiting long-range orientational order without translational periodicity, characterized by crystallographically forbidden rotational symmetries. Although significant progress has been made in understanding atomic quasicrystals, soft-matter systems have emerged as complementary and increasingly important platforms for quasicrystal research. The inherent advantages of soft matter, including tunable interactions, mesoscopic length scales, and direct observability, offer valuable opportunities for investigating quasicrystalline order. Recent years have seen significant advances in soft-matter quasicrystals, from diverse formation mechanisms to unique physical properties. By combining experimental discoveries, simulations, and theoretical perspectives, we organize this review around three connected questions: how soft matter quasicrystals form; what physical principles govern their formation, structure, and stability; and how such order can be rationally designed. While formation pathways provide the entry point of the review, we connect them to broader physical principles and design strategies by discussing competing structural length scales, kinetic pathways, symmetry, tiling constraints, and programmable building blocks. This review is intended to clarify the connections among different soft matter platforms and to identify critical challenges for the rational design and control of quasicrystalline order.