ESPCI web site
Contact geometry in cholesterics and chiral materials
Chirality in materials, such as liquid crystals, often entails a high degree of frustration, leading to a rich array of morphological phenomena. Here I will discuss how methods from contact geometry and topology can be used to give a qualitative understanding of the behaviour of chiral materials. Using experiments on cylindrically confined lyotropic chromonic liquid crystals as a model system, I will show how contact topology-theoretic methods lead to a topological description of the various metastable minima in the energy landscape, as well as explaining the existence of novel chirally-protected solitons. I will further show how the same perspective can be used to understand the structural stability of highly-twisted Skyrmions in chiral ferromagnets, with applications to racetrack memory devices. Finally, I will present the results of transition path sampling calculations describing generic features of chiral morphological transitions in liquid crystalline systems.