Double-atomic-layer Tl-Mg compound on a Si(111) surface with advanced electronic properties

We report on the formation and comprehensive study of atomic and electronic structures of a new Tl-Mg two-dimensional compound reconstruction with $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ periodicity on a Si(111) substrate. Owing to properties of its constituent elements and crystal structure with a breathing kagome lattice of Mg and a dense Tl layer (4/3 monolayer), this double-layer system displays promising features, including spin-split metallic bands, nearly flat bands, and a saddle point with corresponding divergences in the local density of states. These features indicate the possibility that strongly correlated electronic states exist in this structure after tuning the Fermi level position. In accordance with the ${C}_{3}$ symmetry, we observe spin-orbit-coupling-driven Rashba-type spin splitting with spin degeneracy at the $\overline{M}$ point and Zeeman-like splitting at the $\overline{K}$ point. In contrast to the previously reported cases, splitting at the $\overline{K}$ point is significant to produce fully out-of-plane spin-polarized cones. Due to opposite Berry curvatures at the $\overline{K}$ and ${\overline{K}}^{\ensuremath{'}}$ points of the hexagonal surface Brillouin zone, spins at these valleys have opposite signs, which ensure effective spin-pseudospin coupling.