Magnetic response of topological insulator layer with metamaterial substrate induced by an electric point source

Topological insulators (TIs) are materials with unique surface conductive properties that distinguish them from normal insulators and have attracted significant interest due to their potential applications in electronics and spintronics. However, their weak magnetic field response in traditional setups has limited their practical applications. Here, we show that integrating TIs with active metamaterial substrates can significantly enhance the induced magnetic field by more than $10^4$ times. Our results demonstrate that selecting specific permittivity and permeability values for the active metamaterial substrate optimizes the magnetic field at the interface between the TI layer and the metamaterial, extending it into free space. This represents a substantial improvement over previous methods, where the magnetic field decayed rapidly. The findings reveal that the TI-metamaterial approach enhances the magnetic field response, unveiling new aspects of TI electromagnetic behavior and suggesting novel pathways for developing materials with tailored electromagnetic properties. The integration of metamaterials with TIs offers promising opportunities for advancements in materials science and various technological applications. Overall, our study provides a practical and effective approach to exploring the unique magnetic field responses of TIs, potentially benefiting other complex material systems.