Cholesteric blue phases (BPs) are complex three-dimensional structures exhibited by a chiral liquid crystal. BPs comprise a regular array of line defects of orientational order (disclination lines) and double-twist cylinders where the orientational order is twisted along all the directions perpendicular to the cylinder axis. BPs have attracted the interest of physicists as a fascinating example of order induced by frustration, here between the locally favorable double-twist ordering, and global constraints that prohibits double-twist ordering to fill the whole space without singularities.

In this talk we present two studies on how geometric frustrations affect the structures of already frustrated BPs. One concerns the behavior of BPs confined by two parallel flat substrates. The interaction between confining surfaces and the liquid crystal (surface anchoring) frustrates the ordering of BPs, and numerical calculations based on a continuum theory demonstrate the formation of various exotic structures not found in bulk BPs. We particularly focus on the formation of half-Skyrmions, swirl-like order without singularity that has been found in diverse condensed matter systems. We discuss the dynamics of half-Skyrmions driven by thermal fluctuations, and how they are observed experimentally.

The other subject is on the frustration by the mismatch of the lattice orientations of BP leading to twin boundaries. Twinning of BPs like martensites has been revealed in recent experiments, but real-space fine structures of twin boundaries are difficult to observe experimentally. Again systematic numerical calculations based on a continuum theory clarify how two BP lattices with different lattice orientation should be connected. We also present our recent attempts towards the dynamics of phase transition associated with twin formation.

References:
A. Nych, J. Fukuda et al., Nature Phys. 13, 1215 (2017).
J. Fukuda et al., Ann. Phys. 534, 2100336 (2022) (Review article).
A. Yamashita and J. Fukuda, Phys. Rev. E 105, 044707(1-9) (2022).

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