Soft Matter Macro and Micro-Photonics workshop

Time-crystalline order in chiral nematic liquid crystals

Ivan I. Smalyukh1,2,3,4

1 Department of Physics, University of Colorado, Boulder, CO 80309, USA

2 International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM²), Hiroshima University, Higashi Hiroshima, Hiroshima 739-8526, Japan

3 Materials Science and Engineering Program, University of Colorado, Boulder, CO 80309, USA

4 Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309, USA

Time crystals are unexpected states of matter that spontaneously break time-translation symmetry either in a discrete or continuous manner. However, spatially mesoscale space-time crystals that break both space and time symmetries have not been reported. By considering out-of-equilibrium systems, this presentation will report the observation of continuous space–time crystals and discrete space–time crystals generated from topological particle-like solitons in chiral liquid crystal systems [1,2]. Particularly in the discrete space–time crystals, the underlying dynamic mechanism is governed by the transformation between nematic defects resembling Majorana-like quasiparticles and their antiparticles. These findings broaden the possibilities for exploring frontier topics in fundamental physics and reveal the ability of liquid crystals to serve as a bridge between diverse physical platforms within the time crystal research field.

[1] H. Zhao, & I. I. Smalyukh, Space-time crystals from particle-like topological solitons. Nat. Mater. 24, 1802–1811 (2025).

[2] H. Zhao, R. Zhang, & I. I. Smalyukh, Emergent discrete space-time crystal of Majorana-like quasiparticles in chiral liquid crystals. arXiv preprint arXiv:2507.16977, (2025).