Coordination-related, two-dimensional (2D) structural phase transitions are a fascinating 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 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 phase transition from a threefold coordinated onto a fivefold coordinated structure takes place at finite temperature. On unstrained samples, this phase transition requires lattice parameters to evolve freely. A fundamental energy scale $J$ permits understanding this transition, and numerical results indicate a transition temperature $T_c$ of about $1.41J$. Numerical data provides a relation among the experimental (rhombic) parameter $\langle \mathrm{\Delta }\alpha \rangle$ [Chang et al., Science 353, 274 (2016)] and $T$ of the form $\langle \mathrm{\Delta }\alpha \rangle =\mathrm{\Delta }\alpha (T=0){\left(1-T/T_c\right)}^{\beta }$, with a critical exponent $\beta \simeq 1/3$ that coincides with experiment. It is also shown that $\langle \mathrm{\Delta }\alpha \rangle$ is temperature independent in another theoretical work [Fei et al., Phys. Rev. Lett. 117, 097601 (2016)], and thus incompatible with experiment. $T_c$ 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 qualitatively. An analysis of out-of-plane fluctuations and a discussion of the need for van der Waals corrections to describe these materials are given too. These results provide an experimentally compatible framework to understand structural phase transitions in 2D materials and their effects on material properties.

• Received 3 October 2017
• Revised 13 December 2017

DOI:https://doi.org/10.1103/PhysRevB.97.024110