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 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 Tc 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. arXiv:1709.04581v1 [cond-mat.mes-hall]

We performed density functional theory calculations with self-consistent van der Waals corrected exchange-correlation (XC) functionals to capture the structure of black phosphorus and twelve monochalcogenide monolayers and find the following results: (a) The in-plane unit cell changes its area in going from the bulk to a monolayer. The change of in-plane distances implies that bonds weaker than covalent or ionic ones are at work within the monolayers themselves. This observation is relevant for the prediction of the critical temperature Tc. (b) There is a hierarchy of independent parameters that uniquely define a ground state ferroelectric unit cell (and square and rectangular paraelectric unit cells as well): only 5 optimizable parameters are needed to establish the unit cell vectors and the four basis vectors of the ferroelectric ground state unit cell, while square and rectangular paraelectric structures are defined by only 3 or 2 independent optimizable variables, respectively. (c) The reduced number of independent structural variables correlates with larger elastic energy barriers on a rectangular paraelectric unit cell when compared to the elastic energy barrier of a square paraelectric structure. This implies that Tc obtained on a structure that keeps the lattice parameters fixed (for example, using an NVT ensemble) should be larger than the transition temperature on a structure that is allowed to change in-plane lattice vectors (for example, using the NPT ensemble). (d) The dissociation energy (bulk cleavage energy) of these materials is similar to the energy required to exfoliate graphite and MoS2. (e) There exists a linear relation among the square paraelectric unit cell lattice parameter and the lattice parameters of the rectangular ferroelectric ground state unit cell. These results highlight the subtle atomistic structure of these novel 2D ferroelectrics.

Traditional ferroelectrics undergo thermally-induced phase transitions whereby their structural symmetry increases. The associated higher-symmetry structure is dubbed paraelectric. Ferroelectric transition metal dichalcogenide bilayers have been recentlyshown to become paraelectric, but not much has been said of the atomistic configuration of such a phase. As discovered through numerical calculations that include molecular dynamics here, their paraelectricity can only be ascribed to a time average of ferroelectric phases with opposing intrinsic polarizations, whose switching requires macroscopically large areas to slip in unison.

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