Coexistence of Multiple Topological Phases and High-Order Topology in 2D V2CS2, Cr2CS2, and Mn2CS2

This study investigates the topological properties of 2D $V_2{\mathrm{CS}}_2$, ${\mathrm{Cr}}_2{\mathrm{CS}}_2$, and ${\mathrm{Mn}}_2{\mathrm{CS}}_2$ using first-principles calculations. The rare coexistence of different topological fermion types is uncovered within single materials: $V_2{\mathrm{CS}}_2$ hosts both type-I and type-II Dirac points, while the spin-down channel of ferromagnetic ${\mathrm{Cr}}_2{\mathrm{CS}}_2$ exhibits both type-I and type-II Weyl points. In contrast, ${\mathrm{Mn}}_2{\mathrm{CS}}_2$ is identified as an antiferromagnetic insulator (gap $\sim$375 meV), and the spin-up channel of ${\mathrm{Cr}}_2{\mathrm{CS}}_2$ is insulating (gap $\sim$28 meV). We demonstrate that biaxial strain can tune the fermion topology, transforming type-II into type-III fermions, while type-I fermions remain robust. Spin-orbit coupling (SOC) induces gaps at type-I points ($\sim$20-24 meV) but leaves type-II fermions gapless, indicating their robustness against SOC. Furthermore, the spin-up channel of ${\mathrm{Cr}}_2{\mathrm{CS}}_2$ and ${\mathrm{Mn}}_2{\mathrm{CS}}_2$ is identified as magnetic high-order topological insulators (HOTIs). This is confirmed by calculations of quantized fractional corner charges (e/3) protected by $C_3$ symmetry and the identification of topological corner states using tight-binding models. These findings reveal a rich topological landscape in these materials, offering potential for fundamental research and applications in spintronics and quantum computing.