Group-IV monochalcogenide monolayers: Two-dimensional ferroelectrics with weak intralayer bonds and a phosphorenelike monolayer dissociation energy

Abstract

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, which are independent of XC choice: (a) The in-plane unit cell changes its area in going from the bulk to a monolayer. Such structural behavior is unlike the one seen in more traditional two-dimensional materials such as graphene or ${\mathrm{MoS}}_{2}$, in which monolayers keep their structure upon exfoliation. The change of in-plane distances implies that bonds weaker than covalent or ionic ones are at work within the monolayers themselves and may require corrections beyond PBE XC. This observation is relevant for the prediction of the critical temperature ${T}_{c}$ and important for that reason. (b) There exists 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 three or two 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 ${T}_{c}$ 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) Surprisingly, the dissociation energy (bulk cleavage energy) of these materials is similar to the energy required to exfoliate graphite and ${\mathrm{MoS}}_{2}$. (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 and chemical bond of these novel 2D ferroelectrics.