# Theory of helicoids and skyrmions in confined cholesteric liquid crystals

## TL;DR

This paper develops a theoretical framework for understanding complex topological defect structures like helicoids and skyrmions in confined cholesteric liquid crystals, providing exact and numerical solutions that elucidate their formation and stability.

## Contribution

It extends previous theories by deriving exact solutions for helicoids with constant azimuth and numerical solutions for varying azimuth, enhancing understanding of defect structures in confined cholesterics.

## Key findings

- Exact solutions for helicoids with constant azimuth
- Numerical solutions for helicoids and skyrmions with varying azimuth
- Interpretation of defect structures through free energy competition

## Abstract

Cholesteric liquid crystals experience geometric frustration when they are confined between surfaces with anchoring conditions that are incompatible with the cholesteric twist. Because of this frustration, they develop complex topological defect structures, which may be helicoids or skyrmions. We develop a theory for these structures, which extends previous theoretical research by deriving exact solutions for helicoids with the assumption of constant azimuth, calculating numerical solutions for helicoids and skyrmions with varying azimuth, and interpreting the results in terms of competition between terms in the free energy.