Theory of helicoids and skyrmions in confined cholesteric liquid crystals

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.