Introduction

The past five years have witnessed significant advancements in materials science, particularly in the areas of symmetry, topology, and chirality. This mini-review highlights key trends and discoveries within these domains, focusing on the manipulation of material properties through symmetry breaking, the exploration of topological phases, and the control of chirality at the molecular and supramolecular levels. The review synthesizes findings from selected papers, grouping them into distinct research agendas to showcase the evolution of these fields.

Topological Phases and Symmetry Breaking in Condensed Matter

A major area of progress involves the exploration of topological phases of matter and the role of symmetry in defining and manipulating these phases. Jian-Hua Jiang's group has investigated the bulk-disclination correspondence in topological crystalline insulators, revealing how topological properties are linked to crystal defects like disclinations (Yang Liu et al., 2020, Nature; Yang Liu et al., 2021, Nature). This work emphasizes the importance of considering crystal symmetry in understanding topological phenomena. Benjamin J. Wieder's research group has contributed to the development of magnetic topological quantum chemistry, providing a framework for predicting and classifying topological materials with magnetic order (Luis Elcoro et al., 2020, Nature Communications; Luis Elcoro et al., 2021, Nature Communications).

The concept of altermagnetism, a distinct form of magnetism beyond conventional ferromagnetism and antiferromagnetism, has also gained prominence. T. Jungwirth's team introduced the idea of a phase with nonrelativistic spin and crystal rotation symmetry, expanding our understanding of magnetic ordering (Libor Šmejkal et al., 2020, Physical Review X; Libor Šmejkal et al., 2021, Physical Review X; Libor Šmejkal et al., 2022, Physical Review X). Further research by Zhiqi Liu demonstrated an anomalous Hall effect in altermagnetic ruthenium dioxide (RuO2) (Zexin Feng et al., 2021, Nature Electronics; Zexin Feng et al., 2022, Nature Electronics), while H.J. Elmers's group observed time-reversal symmetry breaking in the band structure of the same material (O. Fedchenko et al., 2023, Science Advances; O. Fedchenko et al., 2024, Science Advances). These findings highlight the potential of altermagnetic materials for spintronic applications. Yugui Yao's group has also investigated the crystal thermal transport in altermagnetic RuO2 (Xiaodong Zhou et al., 2023, Physical Review Letters; Xiaodong Zhou et al., 2024, Physical Review Letters).

The exploration of topological phenomena extends to other systems, including photonic and acoustic crystals. Bo Zhen's group has studied quadrupole topological photonic crystals, demonstrating novel ways to control light propagation (Li He et al., 2020, Nature Communications). Baile Zhang's research has focused on projectively enriched symmetry and topology in acoustic crystals (Haoran Xue et al., 2021, Physical Review Letters; Haoran Xue et al., 2022, Physical Review Letters), and Zhen Gao's group has investigated spinful topological phases in acoustic crystals with projective PT symmetry (Yan Meng et al., 2023, Physical Review Letters). Wladimir A. Benalcazar's group has also studied topological phases of photonic crystals under crystalline symmetries (Sachin Vaidya et al., 2023, Physical review. B./Physical review. B). These studies highlight the versatility of topological concepts across different physical systems.

Chirality: From Molecular Assembly to Macroscopic Properties

Another significant area of advancement is the control and manipulation of chirality in materials. Quan Li's group has extensively studied supramolecular chirality transfer towards chiral aggregation (Shuai Huang et al., 2020, Advanced Science; Shuai Huang et al., 2021, Advanced Science), including solvent polarity driven helicity inversion (Qiang Ye et al., 2020, Chemical Science) and photo-triggered circularly polarized luminescence (Siyang Lin et al., 2023, Nature Communications). Pengyao Xing's group has explored chiroptical helices of N-terminal aryl amino acids (Zhuoer Wang et al., 2020, Angewandte Chemie International Edition) and reviewed circularly polarized light responsive materials (Yiping Liu et al., 2023, Advanced Materials). Guofeng Liu's group has focused on metallophilic interaction-mediated hierarchical assembly and dynamic chirality inversion in supramolecular polymers (Longfei Yao et al., 2023, ACS Nano) and full-color circularly polarized luminescence of supramolecular polymers (Kuo Fu et al., 2024, ACS Nano).

The use of liquid crystals to control chirality and circularly polarized luminescence has also been a focus. Weihong Zhu's group has demonstrated liquid crystal assembly for ultra-dissymmetric circularly polarized luminescence (Yue Wu et al., 2022, Journal of the American Chemical Society; Yue Wu et al., 2023, Journal of the American Chemical Society). Wei Zhang's group has achieved switchable phase helicity independent of the absolute configuration of the stereocenter in chiral liquid-crystalline polymers (Xiaoxiao Cheng et al., 2023, Journal of the American Chemical Society). Fusheng Zhang's and Guangyan Qing's groups have created intense left-handed circularly polarized luminescence in chiral nematic hydroxypropyl cellulose composite films (Yuxiao Huang et al., 2024, Advanced Materials). Oleg D. Lavrentovich's group has investigated chiral ground states of ferroelectric liquid crystals (Priyanka Kumari et al., 2024, Science), while Przemysław Kula's and Damian Pociecha's groups have studied spontaneous chiral symmetry breaking in polar fluid-heliconical ferroelectric nematic phase (Jakub Karcz et al., 2024, Science).

Finally, Woo-Sik Kim's group has explored chiral symmetry breaking of sodium chlorate in a Taylor vortex flow (Bowen Zhang et al., 2024, Crystal Growth & Design).

Time Crystals and Non-Equilibrium Phenomena

The study of time crystals, a novel phase of matter that breaks time-translation symmetry, has also seen significant progress. Andreas Hemmerich's and Hans Keßler's groups have reported the observation of a continuous time crystal (Phatthamon Kongkhambut et al., 2020, Science; Phatthamon Kongkhambut et al., 2021, Science; Phatthamon Kongkhambut et al., 2022, Science). Hossein Taheri's group has explored all-optical dissipative discrete time crystals (Hossein Taheri et al., 2021, Nature Communications; Hossein Taheri et al., 2022, Nature Communications). Stephan Rachel's group has achieved the realization of a discrete time crystal on 57 qubits of a quantum computer (Philipp Frey et al., 2021, Science Advances; Philipp Frey et al., 2022, Science Advances). Nikolay I. Zheludev's group has created a photonic metamaterial analogue of a continuous time crystal (Tongjun Liu et al., 2023, Nature Physics). Sai Vinjanampathy's group has explored measurement-induced continuous time crystals (Midhun Krishna et al., 2023, Physical Review Letters).

Conclusion

The research highlighted in this mini-review demonstrates the rapid progress in understanding and manipulating materials through symmetry, topology, and chirality. From the discovery of novel magnetic phases like altermagnetism to the creation of time crystals and the precise control of chirality in supramolecular assemblies, these advancements are paving the way for new technologies and a deeper understanding of the fundamental properties of matter. Further research is needed to explore the full potential of these concepts and to translate these discoveries into practical applications.