  The ability to construct 2D systems, beyond materials natural formation,
enriches the search and control capability of new phenomena. For instance, the
synthesis of topological lattices of vacancies on metal surfaces through
scanning tunneling microscopy. In the present study we demonstrate that metal
atoms encaged in silicate adlayer on silicon carbide is an interesting platform
for lattices design, providing a ground to experimentally construct
tight-binding models on an insulating substrate. Based on the density
functional theory, we have characterized the energetic and the electronic
properties of 2D metal lattices embedded in the silica adlayer. We show that
the characteristic band structures of those lattices are ruled by surface
states induced by the metal-$s$ orbitals coupled by the host-$p_{xy}$ states;
giving rise to $sp_{xy}$ Dirac bands neatly lying within the energy gap of the
semiconductor substrate.
