Searching repulsive Casimir forces between magneto-electric materials

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. To enhance the comprehension of the role of parity symmetry and time-reversal symmetry in determining the sign of the Casimir force, we calculate the Casimir forces between magneto-electric materials and obtain a phase diagram governing the sign of symmetry-breaking-induced Casimir forces. We also investigate how the force phase diagram varies with the separation distances between the objects. Our results contribute to a better understanding of the sign of the Casimir force, a subject bearing both theoretical interest and practical significance.