Charge density waves and surface Mott insulators for adlayer structures on semiconductors: extended Hubbard modeling

Motivated by the recent experimental evidence of commensurate surface charge density waves (CDW) in Pb/Ge(111) and Sn/Ge(111) sqrt{3}-adlayer structures, as well as by the insulating states found on K/Si(111):B and SiC(0001), we have investigated the role of electron-electron interactions, and also of electron-phonon coupling, on the narrow surface state band originating from the outer dangling bond orbitals of the surface. We model the sqrt{3} dangling bond lattice by an extended two-dimensional Hubbard model at half-filling on a triangular lattice. We include an on-site Hubbard repulsion U and a nearest-neighbor Coulomb interaction V, plus a long-ranged Coulomb tail. The electron-phonon interaction is treated in the deformation potential approximation. We have explored the phase diagram of this model including the possibility of commensurate 3x3 phases, using mainly the Hartree-Fock approximation. For U larger than the bandwidth we find a non-collinear antiferromagnetic SDW insulator, possibly corresponding to the situation on the SiC and K/Si surfaces. For U comparable or smaller, a rich phase diagram arises, with several phases involving combinations of charge and spin-density-waves (SDW), with or without a net magnetization. We find that insulating, or partly metallic 3x3 CDW phases can be stabilized by two different physical mechanisms. One is the inter-site repulsion V, that together with electron-phonon coupling can lower the energy of a charge modulation. The other is a novel magnetically-induced Fermi surface nesting, stabilizing a net cell magnetization of 1/3, plus a collinear SDW, plus an associated weak CDW. Comparison with available experimental evidence, and also with first-principle calculations is made.