Intrinsic Instabilities and Mechanical Anisotropy in Halide Perovskite Monolayers

Abstract

Halide perovskites have been extensively studied owing to their excellent optoelectronic properties and their unique lattice characteristics, that are very soft and anharmonic. Recent studies indicate the importance of a deep understanding of their surfaces and, in the limit, the properties of low-dimensional structures based on these materials. To investigate the structural and electronic properties of halide perovskite monolayers (i.e., perovskenes), this work uses first-principles simulations. We have studied three different stoichiometries (ABX3, ABX4, and A2BX4) and structural phases for iodide, bromide, and chloride perovskite monolayers. Their thermodynamic behavior was evaluated through the construction of phase diagrams, highlighting the instability of the ABX4 stoichiometry, which was further supported by its mechanical instability. Structurally, the covalent characteristics of the Pb--X bond, in contrast to the Cs--X bonds, induce a strong anisotropy in the Young's modulus and Poisson's ratio along different crystallographic directions, and also account for the lower stiffness observed in the phases where the octahedra are not aligned. The electronic properties are somewhat similar to those of their 3D counterparts, but with a slightly larger band gap; in the monolayers, the band gap increases with halogen electronegativity (I, Br, Cl) and octahedral tilting. Moreover, the non-symmetric ABX3 stoichiometry exhibited a spin splitting due to the internal dipole moment in these layers. Overall, our work lays the groundwork for a deeper understanding of low-dimensional structures based on halide perovskites.

Figures (6)

• Figure 1: Structural difference between the (a) ABX$_3$, (b) ABX$_4$, and (c) A$_2$BX$_4$ monolayers. Energy differences relative to the M-Quadratic phase for the phases (d) M-Quadratic, (e) P-Rectangular, (f) P-Square, and (g) P-OBlique. The thermodynamic stability of the octahedral tilting is evidenced. Each color represents a halide, as showed in the labels. Finally, each stoichiometry is grouped in sets of 3 bars. The most stable phases for ABX$_3$ and ABX$_4$ are the P-Oblique structures, whereas for A$_2$BX$_4$ the P-Rectangular phase is favored. Atomic structures of each studied phase are shown in panels (e--h).
• Figure 2: Phase diagrams comparing stoichiometries. Each diagram represents the behavior of (a) Iodides, (b) Bromides, and (c) Chlorides. The filled areas represent the regions where each stoichiometry is thermodynamically stable. These results indicate the thermodynamic instability of the ABX$_4$ stoichiometry.
• Figure 3: Young’s modulus ($Y^{2D}$) and Poisson’s ratio ($\nu^{2D}$) for (a, d) ABX$_3$ (P-Oblique), (b, e) ABX$_4$ (M-Quadratic), and (c, f) A$_2$BX$_4$ (P-Rectangular), respectively. The angles represent the different crystalline directions and the colors represent the different halogens, which do not significantly affect the mechanical properties. Octahedral tilting and monolayer stoichiometry play a crucial role in determining both Young’s modulus and Poisson’s ratio. In the Square and Oblique phases, the Pb-X bonds are aligned along the 0$^\circ$, 90$^\circ$, 180$^\circ$, and 270$^\circ$ directions, and the X-X bonds are in the 45$^\circ$, 135$^\circ$, 225$^\circ$, and 315$^\circ$ directions. In the rectangular phases, the behavior is inverted, with the X-X bonds along the 0$^\circ$, 90$^\circ$, 180$^\circ$, and 270$^\circ$, and the Pb-X bonds in the 45$^\circ$, 135$^\circ$, 225$^\circ$, and 315$^\circ$ directions.
• Figure 4: Partial density of states for CsPbI$_3$ bulk (a) and Cs$_2$PbI$_4$ monolayer (b) at PBE functional level. Schematic representation of molecular orbitals for (c) bulk and (d) monolayer halide perovskites. The states were aligned by the energy of the Cs-5s orbital.
• Figure 5: Planar-averaged electrostatic potential along the $z$ direction for CsPbI$_3$ and Cs$_2$PbI$_4$ stoichiometries (a--b). Electronic band structures (c--d) with HSE06 and SOC for CsPbI$_3$ and Cs$_2$PbI$_4$ stoichiometries in the P-Oblique and P-Rectangular phases, respectively. Scheme (e) shown a energy contour line relative to the CsPbI$_3$ monolayer, representing the spin orientations around the reciprocal space. Graphic (f) presents new DFT calculations, considering the SOC, for CsPbI$_3$ monolayer through the path Y $\rightarrow \Gamma \rightarrow$ -Y, confirming the Rashba-characteristic spin splitting in this monolayer.