  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.
