Emergence of Van Hove singularity and topological states in Pb3Bi/Ge(111) Rashba systems

It has been shown recently that the coexistence of Van Hove singularity and geometric phase in ${\mathrm{Pb}}₃\mathrm{Bi}\text{/}\mathrm{Ge}(111)$ as a prototypical Rashba system can result in chiral topological superconductivity [W. Qin, L. Li, and Z. Y. Zhang, Nat. Phys. 15, 796 (2019)]. Here, we use first-principles calculations to systematically investigate the structural, electronic, and topological properties of the ${\mathrm{Pb}}₃\mathrm{Bi}\text{/}\mathrm{Ge}(111)$ alloyed systems by considering not only the configuration that harbors topological superconductivity considered previously (labeled as the ${\mathrm{T}}₁$ phase) but also two other energetically nearly degenerate configurations with high symmetries (labeled as ${\mathrm{H}}₃$ and ${\mathrm{T}}₄$). We first show that all the three structural configurations have giant Rashba-type spin splittings, resulting from the strong spin-orbit coupling effect of the heavy elements (Pb, Bi) together with inversion symmetry breaking. Next, we demonstrate that each of the saddle- or paraboliclike band dispersions can lead to the emergence of Van Hove singularities, whose positions can be substantially tuned by the giant Rashba effect to the vicinity of the Fermi level. Furthermore, we reveal the existence of topological states in both the ${\mathrm{H}}₃$ and ${\mathrm{T}}₄$ phases, and the corresponding Rashba-induced band gaps are given by 25 and 50 meV, respectively. Given the energetic affinity of the three phases, these findings suggest the feasibility of realizing quantum phase transitions between quantum spin Hall effect and topological superconductivity within the same materials platform. The present study is expected to give new insights in searching for topological quantum states including 2D topological superconductivity based on Rashba systems.