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Significance A material’s topology is more than its shape. It governs the material’s physical properties, such as how it interacts with acoustic waves and transports charge carriers. Utilizing liquid crystals (LCs) and their defects, researchers have pursued understanding topological aspects of condensed matter. Our work discusses the topological properties of cholesteric LCs that twist spontaneously. The traditional topological descriptions of LC do not extend to a complete characterization of cholesterics, and yet they often exhibit behavior with a strong topological and geometric character. We show that a more subtle chiral topology, protected by nonvanishing twist, can be used to define new topological numbers and understand these systems’ behavior, including the metastability, layering transitions, and soliton structures that traditional invariants cannot describe.

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement