C$_{60}$-Induced Devil's Staircase Transformation on Pb/Si(111) Wetting Layer

Density functional theory is used to study structural energetics of Pb vacancy cluster formation on C$_{60}$/Pb/Si(111) to explain the unusually fast and error-free transformations between the ``Devil's Staircase'' (DS) phases on the Pb/Si(111) wetting layer at low temperature (\textasciitilde 110 K). The formation energies of vacancy clusters are calculated in C$_{60}$/Pb/Si(111) as Pb atoms are progressively ejected from the initial dense Pb wetting layer. Vacancy clusters larger than 5 Pb atoms are found to be stable with 7 being the most stable, while vacancy clusters smaller than 5 are highly unstable, which agrees well with the observed ejection rate of \textasciitilde 5 Pb atoms per C$_{60}$. The high energy cost (\textasciitilde 0.8 eV) for the small vacancy clusters to form indicates convincingly that the unusually fast transformation observed experimentally between the DS phases, upon C$_{60}$ adsorption at low temperature, cannot be the result of single-atom random walk diffusion but correlated multi-atom processes.