Interplay of Electronic Orders in Topological Quantum Materials

Topological quantum materials hold great promise for future technological applications. Their unique electronic properties, such as protected surface states and exotic quasi-particles, offer opportunities for designing novel electronic and spintronics devices and allow quantum information processing. The origin of the interplay between various electronic orders in topological quantum materials, such as superconductivity and magnetism, remains unclear, particularly whether these electronic orders cooperate, compete, or simply coexist. Since the 2000s, the combination of topology and matter has sparked a tremendous surge of interest among theoreticians and experimentalists alike. Novel theoretical descriptions and predictions as well as complex experimental setups confirming or refuting these theories continuously appear in renowned journals. This review aims to provide conceptual tools to understand the fundamental concepts of this ever-growing field. Superconductivity and its historical development will serve as a second pillar alongside topological materials. While the main focus of this review is topological materials such as topological insulators and semimetals, topological superconductors will be explained phenomenologically.