Exotic structures of a thin film of chiral liquid crystals: a numerical study based on the Landau–de Gennes theory

Abstract

Chiral liquid crystals exhibit various intriguing ordered structures arising from helical distortions of the orientational order allowed by chirality. We present our numerical studies on such exotic structures of chiral liquid crystals, particularly focusing on those in a thin film whose thickness is on the order of or smaller than the characteristic helical pitch of the liquid crystal. We first review the Landau–de Gennes continuum theory we use in our calculations, in which the orientational order is described by a second-rank tensor $Q_{\alpha \text{β}}$ and the free energy of a liquid crystal is given as a functional of $Q_{\alpha \text{β}}$. We show that a thin film of a chiral liquid crystal can exhibit a diverse variety of ordered structures involving topological line defects (disclination lines), depending on film thickness, temperature, and type of surface anchoring (normal, planar, and planar degenerate). Such exotic structures include a hexagonal lattice of Skyrmions, a whirl-like localized structure that finds in its place in a wide variety of condensed matter systems. A thin film of a chiral liquid crystal thus provides an interesting platform for the investigation of exotic structures of orientational order arising from the frustration between the bulk ordering and the spatial confinement with surface anchoring.

Keywords:

• Chiral liquid crystal
• thin film
• numerical calculation
• Landau–de Gennes theory
• topological defect
• Skyrmion

Acknowledgments

The author thanks Professor Oleg D. Lavrentovich for giving him the opportunity to contribute this article and helpful comments before submission. He also thanks Professor Slobodan Žumer for valuable discussions, encouragement, and generous support that enabled him to stay in University of Ljubljana, during which important part of his work was carried out. He also thanks Dr. Andriy Nych, Dr. Uliana Ognysta and Professor Igor Muševič whose experiments motivated part of his study. Part of numerical calculations was carried out at the Supercomputer Center, the Institute for Solid State Physics, the University of Tokyo.

Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Disclosure statement

The author declares no conflict of interest.

Additional information

Funding

J.F. is supported by Slovenian Research Agency (ARRS research program P1-0099 and project J1-2335 and J1-2325), the Center of Excellence NAMASTE, JSPS KAKENHI (Grant Numbers JP25400437, JP17H02947 and JP21H01049), the Cooperative Research Program of “Network Joint Research Center for Materials and Devices” (Grant Numbers 20201297 and 20211329).