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

TL;DR

This study models surface charge density waves and Mott insulators on semiconductor adlayers using an extended Hubbard model, revealing how electron interactions influence surface electronic phases and structures.

Contribution

It introduces a comprehensive extended Hubbard model including electron-electron and electron-phonon interactions to analyze surface adlayer phases on semiconductors.

Findings

Magnetic insulators form when U exceeds the bandwidth.

Inter-site V stabilizes metallic charge density wave phases.

Model explains experimental surface structures and insulating states.

Abstract

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.