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Twisted bilayered graphenes at magic angles are systems housing long rangedperiodicity of Moir\'e pattern together with short ranged periodicityassociated with the individual graphenes. Such materials are a fertile groundfor novel states largely driven by electronic correlations. Here we find thatthe ubiquitous Casimir force can serve as a platform for macroscopicmanifestations of the quantum effects stemming from the magic angle bilayeredgraphenes properties and their phases determined by electronic correlations. Byutilizing comprehensive calculations for the electronic and optical response,we find that Casimir torque can probe anisotropy from the Drude conductivitiesin nematic states, while repulsion in the Casimir force can help identifytopologically nontrivial phases in magic angle twisted bilayered graphenes.

Twisted bilayered graphenes at magic angles and Casimir interactions: correlation-driven effects