Formation of a quantum spin Hall state on a Ge(111) surface

Using first-principles density functional theory (DFT) hybrid functional calculations, we demonstrate the formation of a quantum spin Hall (QSH) state on a Ge(111) surface. We show that a 1/3 monolayer (ML) Cl-covered Ge(111) surface offers an ideal template for metal, such as Bi, deposition into a stable hexagonal overlayer 2D lattice, which we refer to as Bi@Cl-Ge(111). The band structure and band topology of Bi@Cl-Ge(111) are analyzed with respect to the effect of spin-orbit coupling (SOC). The Bi@Cl-Ge(111) exhibits a QSH state with a band gap of 0.54 eV. In contrast, the Au@Cl-Ge(111) is found to be a trivial semiconducting surface. The Ge(111) substrate acts as an orbital filter to critically select the orbital composition around the Fermi level. Our findings offer another possible system for experimental exploration of the growth of 2D topological materials on conventional semiconductor substrates, where the 2D overlayer is atomically bonded to, but electronically decoupled from, the underlying substrate, exhibiting an isolated topological quantum state inside the substrate band gap.