Résumé
Thermal fluctuations are a very common feature of soft matter systems, and generally carry information about the structures and dynamics of the studied materials. In liquid crystals, these fluctuations are commonly studied in a dynamic light scattering (DLS) setup, and can be used, for example, to measure the elastic constants of a nematic phase. Indeed, De Gennes showed that the fluctuation modes of an unbound uniformly aligned nematic take the simple form of Fourier modes associated with relaxation times depending on the nature of the deformation (splay-bend or twist-bend) [1].In the more general case of nonuniform and/or confined phases, the translational invariance of unbound nematic is broken and the fluctuation modes couple with the local structures defining the liquid crystal phase or the confining surfaces [2,3]. For example, a critical slowing down of fluctuation modes in highly confined samples of blue phase III was recently observed and analysed, due to a transformation of the 3D skyrmionic fluid into a quasi 2D skyrmionic lattice [4]. As a general rule, confinement plays a major role in the nature and dynamics of fluctuation modes, and can even lead to exotic effect such as Casimir forces [5]. Interestingly, the fluctuation modes of unwound frustrated cholesterics were never analysed in depth, at least to the best of my knowledge. This frustrated phase can typically be obtained by confining a cholesteric layer between two plates with strong uniform anchoring, with a thickness smaller than half the cholesteric pitch. It supports the existence of fascinating chiral topological states localized in the uniformly aligned background director field [6].In this contribution, I show that despite the similarity between the director fields of fully unwound cholesterics and uniformly aligned nematics, hidden traces of chirality can still be found in the fluctuation modes of the former system. I demonstrate the existence of a soft chiral fluctuation mode which critically slows down near the unwinding transition threshold. I also propose a simple microscopy setup to measure the associated relaxation times without any need for a complex DLS setup. Such a setup can be used to measure the local value of the equilibrium cholesteric pitch, even though the director field is fully unwound here.The author acknowledges enlightening discussions with Slobodan Žumer about Casimir effects, fluctuations and light scattering.[1] P. G. De Gennes, J. Prost, The physics of liquid crystals, (Oxford University Press, 1993).[2] C. Fan, L. Kramer, M. J. Stephen, Physical Review A, 2, 2482 (1970).[3] B. Y. Zel’dovich, N. V. Tabiryanl, Zh. Eksp. Teor. Fiz., 81, 1738 (1981).[4] J. Pišljar et al., Physical Review X, 12, 011003 (2022).[5] P. Ziherl F. K. P. Haddadan, R. Podgornik, S. Žumer, Physical Review E, 61, 5361 (2000).[6] P. Ackerman, I. Smalyukh, Physical Review X, 7, 011006 (2017).