  Here, we show that the electronic properties of a surface-supported
2-dimensional (2D) layer structure can be self-texturized at the nanoscale. The
local electronic properties are determined by structural relaxation processes
through variable adsorption stacking configurations. We demonstrate that the
spatially modulated layer-buckling, which arises from the lattice mismatch and
the layer/substrate coupling at the GdAu2/Au(111) interface, is sufficient to
locally open an energy gap of ~0.5eV at the Fermi level in an otherwise
metallic layer. Additionally, this out-of-plane displacement of the Gd atoms
patterns the character of the hybridized Gd-d states and shifts the center of
mass of the Gd 4f multiplet proportionally to the lattice distortion. These
findings demonstrate the close correlation between the electronic properties of
the 2D-layer and its planarity. We demonstrate that the resulting template
shows different chemical reactivity which may find important applications.
