Intrinsic Character of the $(3\times 3)$ to $(\sqrt{3}\times \sqrt{3})$ Phase Transition in $\mathrm{P}\mathrm{b}/\mathrm{S}\mathrm{i}(111)$

We have investigated the $(3\times 3)$ to $(\sqrt{3}\times \sqrt{3})$ reversible phase transition in $\mathrm{P}\mathrm{b}/\mathrm{S}\mathrm{i}(111)$ by means of variable temperature scanning tunneling microscopy and density functional first-principles calculations. By tracking exactly the same regions of the surface with atomic resolution in a temperature range between 40 and 200 K, we have observed the phase transition in real time. The ability to prepare and track exceptionally large domains without defects has allowed us to detect the intrinsic character of the phase transition at temperatures around 86 K. This intrinsic character is in full agreement with our first-principles calculations. Moreover, our results show that the hypothesis that point defects play a fundamental role as the driving force, reported for similar systems, can be discarded for $\mathrm{P}\mathrm{b}/\mathrm{S}\mathrm{i}(111)$.