Surface charge density waves and the Mott insulators for 3×3 adlayers on (1 1 1) semiconductor surfaces

We discuss our recent studies on the low-temperature instabilities of the 3×3 phase of tetravalent adatoms on (1 1 1) semiconductor surfaces. The cases of interest include the surface charge density wave (CDW) systems Pb/Ge(1 1 1) and Sn/Ge(1 1 1), as well as the Mott insulators Si/SiC(0 0 0 1) and K/Si(1 1 1):B. We have approached the problem in two ways: first, by employing a one-band model Hamiltonian of the Hubbard–Holstein type, in order to understand general features of the phase diagram as a function of the strength of electron–electron (e–e) and electron–phonon (e–ph) interactions; second, by performing realistic ab initio calculations within the local spin density approximation (LSDA) for the case of Sn/Si(1 1 1), and of a hypothetical 3×3 Si/Si(1 1 1) mimicking K/Si(1 1 1):B. The collinear LSDA calculation for both Sn/Ge(1 1 1) and Si/Si(1 1 1) predicts a spin density wave (SDW) state with a uniform magnetization mz=1/3 and a small secondary CDW. We discuss and stress the likely important role played by e–e interactions in explaining the phenomenology of all these systems, as opposed to the secondary role played by the e–ph coupling, which would at most drive the lattice, for Pb–Sn/Ge(1 1 1), after the electrons have caused the transition.