Tuning the ferro- to para-electric transition temperature and dipole orientation of group-IV monochalcogenide monolayers

Coordination-related, two-dimensional (2D) structural phase transitions are a fascinating and novel facet of two-dimensional materials with structural degeneracies. Nevertheless, a unified theoretical account of these transitions remains absent, and the following points are established through {\em ab-initio} molecular dynamics and 2D discrete clock models here: Group-IV monochalcogenide (GeSe, SnSe, SnTe, ...) monolayers have four degenerate structural ground states, and a 2D phase transition from a three-fold coordinated onto a five-fold coordinated structure takes place at finite temperature. On unstrained samples, the 2D phase transition requires lattice parameters to freely evolve. A fundamental energy scale permits understanding this transition. The transition temperature $T_c$ and the orientation of the in-plane intrinsic electric dipole can be controlled by moderate uniaxial tensile strain, and a modified discrete clock model describes the transition on strained samples. These results establish a general underlying theoretical background to understand structural phase transitions in 2D materials and their effects on material properties.