The Casimir effect, arising from vacuum quantum fluctuations, plays a fundamental role in the development of modern quantum electrodynamics. In parallel, the field of condensed matter has flourished through the discovery of various materials exhibiting broken symmetries, often connected to topology and characterized by magneto-electric coupling. Here, we calculate the Casimir forces between materials with time-reversal symmetry and/or parity symmetry breaking. Remarkably, we obtain a universal phase diagram governing the sign of symmetry-breaking-induced Casimir forces, contributing to a comprehensive understanding on the sign of Casimir force for linear optical materials. The discovered phase diagram serves as a roadmap for searching repulsive Casimir forces, a subject bearing both theoretical interest and practical significance.
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Dai et al. (2024) studied this question.
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