Pressure-induced bonding diversity, electronic topology, and superconducting electrides in Ca-Ge systems

Group IV elements exhibit diverse bonding and crystalline structures, including carbon-based configurations such as graphene and diamond, and silicon-based porous structures. This diversity gives rise to intriguing physical phenomena and applications, such as magic-angle superconductivity and superhard materials. However, the potential configurations formed by germanium and their corresponding physical properties remain largely unexplored. In this study, we employ a crystal structure prediction method to investigate calcium germanide under high pressures, identifying 12 exotic thermodynamically stable phases. Notably, the CaGe systems display a variety of bonding types, with germanium forming zigzag, square ring, armchair, and ladder configurations. Additionally, we found that the known $\mathrm{C}{\mathrm{a}}_{2}\mathrm{Ge}$ system undergoes a metal-insulator phase transition, transforming into a hexagonal structure with nontrivial band topology. For calcium-rich compounds, we discovered several electride phases with distinct cavity shapes. Among these, the $\mathrm{C}{\mathrm{a}}_{4}\mathrm{Ge}$ Imma phase possesses one-dimensional interstitial electrons. It exhibits a superconducting transition temperature of approximately 10 K at 60 GPa, which is higher than other calcium-based electrides at moderate pressures. Our findings demonstrate that introducing metal atoms can induce diverse bonding characteristics in group IV elements, resulting in a wide range of physical properties, including superconducting and topological behaviors.