The Casimir effect has received extensive attention theoretically and experimentally in recent years. It arises from the macroscopic manifestation of quantum vacuum fluctuations, and this Casimir interaction force can be an effective means of driving and controlling components in micro-electro-mechanical system (MEMS) and nano-electromechanical system (NEMS). Due to the new possibilities provided by photonic topological insulator for designing and using photonic devices, in this work, the Casimir force between the multilayer structures of non-reciprocal photonic topological insulators with broken time-reversal symmetry is investigated, and the influences of the dielectric tensor of the photonic topological insulator, the spatial structural parameters of the multilayer system, and the rotational degree of freedom on the Casimir force are examined. It is found that there exists Casimir repulsive force in such a multilayer system, and the Casimir stable equilibrium and restoring force can be further realized and controlled. Continuous variation between anti-mirror-symmetric configuration and mirror-symmetric configuration is examined. Both the Casimir attraction and repulsion can be generally enhanced through structural optimization by increasing layer number and individual layer thickness. Furthermore, we focus on the detailed analysis of how the optical axis angle difference within the photonic topological insulator layers can be used to adjust the Casimir force. The overall relative rotation of the multilayer system may adjust the magnitude and the direction of the Casimir force, and some inflection points can be found from the influence curve of the optical axis angle difference between internal layers of the multilayer on the Casimir force, allowing the rotational degrees of freedom in the multilayer system to be used for fine-adjusting the Casimir interaction. This work introduces the enhanced degrees of freedom for probing and manipulating the interaction between small objects in micro/nano systems, thereby suppressing adverse Casimir forces and effectively using them.
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