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

Theory of helicoids and skyrmions in confined cholesteric liquid crystals