One-dimensional spin-polarized electron channel in the two-dimensional PbBi compound on silicon

Quantum phenomena at the ultimate atomic-scale two-dimensional limit attract increasing interest due to the emergence of exotic physics and potential applications in prospective electronic devices. In this work, we carried out a theoretical and experimental study of the atomic, electronic, and spin structures of the single-atomic-layer PbBi compounds grown on silicon surface. We found that adsorption of half-monolayer of Bi and half-monolayer of Pb onto Si(111) surface leads to the formation of an atomic layer consisting of rhombuslike motifs. The rhombuslike motifs are arranged into the $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$ and $2\ifmmode\times\else\texttimes\fi{}2$ periodical structures. In the $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$-PbBi phase, the motifs are oriented according to the ${C}_{3}$ symmetry and this phase is characterized as a trivial insulating spin-split system. In the $2\ifmmode\times\else\texttimes\fi{}2$-PbBi phase, the motifs are oriented along a single direction giving rise to a one-dimensional metallic spin-polarized electron channel, which is of great relevance for spintronic-based applications. We traced the origin of the one-dimensional electronic states in the two-dimensional PbBi compound and discussed the interplay of these one-dimensional states with the geometry of the phase.