Complex structural phase transition in a defect-populated two-dimensional system

A complex phase transition in Sn/Ge(111) and similar systems can be decomposed into two intertwined phase transitions: a structural symmetry lowering $(\sqrt{3}\times \sqrt{3})(3\mathrm{}\times 3)$ transition and a disorder-order transition in the defect distribution. We present two phenomenological models that describe these transitions and their interrelation. These models allow us to understand the formation of domains and domain walls at low temperatures, defect-induced density waves above the structural transition temperature, and ordering of the defects caused by lattice-mediated defect-defect interactions. The models predict a destruction of the pure structural transition when impurities are introduced into the system, a shift in the structural crossover temperature with impurity density, and a dependence of the $(3\mathrm{}\times 3)$ lattice structure on the specific defect alignment.