Role of defects in two-dimensional phase transitions: An STM study of the Sn/Ge(111) system

The influence of Ge substitutional defects and vacancies on the $(\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3})$$\ensuremath{\rightarrow}(3\ifmmode\times\else\texttimes\fi{}3)$ charge-density wave phase transition in the $\ensuremath{\alpha}$ phase of Sn on Ge(111) has been studied using a variable-temperature scanning tunneling microscope. Above 105 K, Ge substitutional defects stabilize regions with $(3\ifmmode\times\else\texttimes\fi{}3)$ symmetry that grow with decreasing temperature and can be described by a superposition of exponentially damped waves. At low temperatures, $T<~105\mathrm{K}$ defect-defect density-wave-mediated interactions force an alignment of the defects onto a honeycomb sublattice that supports the low-temperature $(3\ifmmode\times\else\texttimes\fi{}3)$ phase. This defect-mediated phase transition is completely reversible. The length scales involved in this defect-defect interaction dictate the domain size $(\ensuremath{\approx}{10}^{4} {\mathrm{\AA{}}\mathrm{}}^{2}).$