Giant director fluctuations in liquid crystal drops

We report the discovery and elucidation of giant spatiotemporal orientational fluctuations in nematic liquid crystal drops with radial orientation of the nematic anisotropy axis producing a central "hedgehog" defect. We study the spatial and temporal properties of the fluctuations experimentally using polarized optical microscopy, and theoretically, by calculating the eigenspectrum of the Frank elastic free energy of a nematic drop of radius R_{2}, containing a spherical central core of radius R_{1} and constrained by perpendicular boundary conditions on all surfaces. We find that the hedgehog defect with radial orientation has a complex excitation spectrum with a single critical mode whose energy vanishes at a critical value μ_{c} of the ratio μ=R_{2}/R_{1}. When μ<μ_{c}, the mode has positive energy, indicating that the radial hedgehog state is stable; when μ>μ_{c}, it has negative energy indicating that the radial state is unstable to the formation of a lower-energy state. This mode gives rise to the large-amplitude director fluctuations we observe near the core, for μ near μ_{c}. A collapse of the experimental data corroborates model predictions for μ<μ_{c} and provides an estimate of the defect core size.