A Universal Roadmap For Searching Repulsive Casimir Forces Between Magneto-Electric Materials

The Casimir effect, one of the famous manifestations of 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, that often connected to topology and characterized by magneto-electric coupling. Here, we calculate the Casimir forces between materials with colossal magneto-electric effect. Remarkably, we obtain a universal phase diagram for the sign of Casimir forces induced by the magneto-electric symmetry-breaking parameters, furnishing a comprehensive understanding on the sign of Casimir force for all linear electromagnetic materials. The discovered phase diagram serves as a roadmap for identifying repulsive Casimir forces, a subject of both theoretical interest and practical significance.