Our photoemission spectroscopy results clearly demonstrate that symmetry breakdown in atomic arrangement brings about a lift of degeneracy in electronic states, leading to settle a long-standing controversy on a surface superstructure. We provide unambiguous evidences that $\mathrm{Si}\mathrm{}\left(111\right)\mathrm{}\sqrt{3}\times \sqrt{3}-\mathrm{Ag}$ has the inequivalent triangle structure (IET), excluding a long-lived honeycomb-chained triangle model. We also give critical experimental proof that the surface exhibits a disorder-order phase transition by cooling; the thermally fluctuating IET structure is frozen.

• Received 2 April 2003

DOI:https://doi.org/10.1103/PhysRevB.68.085407