Sign reversal of Casimir-Lifshitz torque with separation distance: A theoretical guide to experimentation

The Casimir-Lifshitz torque between a pair of birefringent materials was recently shown to exhibit a change in sign with respect to the separation distance owing to the planar dielectric properties of the interacting materials. The recent experiment that verified the existence of the Casimir-Lifshitz torque precluded a sign reversal between the liquid crystal 5CB $(4\text{\ensuremath{-}}\mathrm{cyano}\text{\ensuremath{-}}4\text{\ensuremath{-}}n\text{\ensuremath{-}}\mathrm{pentylbiphenyl})$ and calcite [Somers et al., Nature (London) 564, 386 (2018)]. Here, we will show that the sign reversal was not observed in the experiment because it would happen at a larger distance than was investigated for the pairs of materials considered. The purpose of this paper is to identify appropriate choices of combinations of materials that will facilitate experimental observation of the distance-dependent sign reversal of the torque in the experimentally feasible distance regime. Specifically, we propose a setup comprising biaxial black phosphorus and the liquid crystal 5CB or 5PCH $(4\text{\ensuremath{-}}\mathrm{cyano}\text{\ensuremath{-}}4\text{\ensuremath{-}}n\text{\ensuremath{-}}\mathrm{pentylcyclohexane}\text{\ensuremath{-}}\mathrm{phenyl})$ as a particularly viable option. The feature of sign reversal will be an interesting addition to the control mechanism of actuation and switch devices that are applicable for the Casimir-Lifshitz torque.