Twisted bilayered graphenes at magic angles and their Casimir interactions*

Magic-angle twisted bilayered graphene (MATBG) is emerging as a material with unusual physics resulting from the interplay of long-range periodicity from its moiré patterns and the short-range lattice structure periodicity from each graphene monolayer. Strong correlation effects in MATBG lead to breaking of various symmetries, considered to be an inherent reason for the emergence of superconductivity and nematicity among others. In this work, we consider Casimir phenomena as a means to probe the electronic and optical response of MATBG. Using a generalized Lifshitz approach and advanced electronic structure models for the optical response, the ubiquitous Casimir force is found to exhibit rich physics, such as different scaling laws, repulsion, and quantization for its different phases. A sizable Casimir torque is found for nematic MATBG directly related to the anisotropy of the Drude optical conductivity. Possible experimental measurements of Casimir effects are also discussed. Casimir effects are one of the few macroscopic manifestations of quantum mechanics and they broaden our understanding of light-matter interactions in general.