  In this work we computed the phase diagram as a function of temperature and
doping for a system of lead adatoms allocated periodically on a silicon (111)
surface. This Si(111):Pb material is characterized by a strong and long-ranged
Coulomb interaction, a relatively large value of the spin-orbit coupling, and a
structural phase transition that occurs at low temperature. In order to
describe the collective electronic behavior in the system, we perform many-body
calculations consistently taking all these important features into account. We
find that charge- and spin-density wave orderings coexist with each other in
several regions of the phase diagram. This result is in agreement with the
recent experimental observation of a chiral spin texture in the charge density
wave phase in this material. We also find that geometries of the charge and
spin textures strongly depend on the doping level. The formation of such a rich
phase diagram in the Si(111):Pb material can be explained by a combined effect
of the lattice distortion and electronic correlations.
