The mechanism for the 3×3 distortion of Sn/Ge(111)

We show that two distinct 3×3 ground states — one non-magnetic, metallic and distorted; the other magnetic, semi-metallic (or insulating) and undistorted — compete in α-phase adsorbates on semiconductor (111) surfaces. In Sn/Ge(111), local (spin) density approximation (LSDA) and GGA calculations indicate, in agreement with experiment, that the distorted metallic ground state prevails. The reason for the stability of this state is analysed, and traced to a sort of bond density wave, specifically a modulation of the antibonding state filling between the adatom and a GeGe bond directly underneath.