Computational study of heavy group IV elements (Ge, Sn, Pb) triangular lattice atomic layers on SiC(0001) surface

Group IV heavy elements atomic layers are expected to show an interesting physical properties due to their large spin-orbit coupling (SOC). Using density functional theory (DFT) calculations with/without SOC we investigate the variation of group IV heavy elements overlayers, namely dense triangular lattice atomic layers (TLAL) on the surface of SiC(0001) semiconductor. The possibility of such layers formation and their properties have not been addressed before. Here we show, that these layers may indeed be stable and, owing to peculiar bonding configuration, exhibit robust Dirac-like energy bands originating from $p_x+p_y$ orbitals and localized mostly within the layer, and $p_z$ band localized outside the layer and interacting with SiC substrate. We found that a $T_1$ adsorption site is most favorable for such TLAL structure and this results in an unusual SOC-induced spin polarization of the states around $\bar{K}$ points of Brillouin zone, namely the coexistence of Rashba- and Zeeman-like spin polarization of different states. We explain this phenomena in terms of symmetry of partial electronic density rather than symmetry of atomic structure.