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

Motivated by the recent experimental evidence of commensurate surface 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 dangling bond orbitals of the adsorbate. We model the problem 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 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 the model including the possibility of commensurate 3x3 phases, using mainly the Hartree-Fock approximation. For U larger than the bandwidth we find magnetic insulators, possibly corresponding to the situation in SiC and in K/Si. For smaller U, the inter-site repulsion V can stabilize metallic CDW phases, reminiscent of the 3x3 structures of Sn/Ge, and possibly of Pb/Ge.