Origin of polymorphism of the two-dimensional group-IV monochalcogenides

Abstract

Unlike other two-dimensional (2D) isovalent materials, the 2D group IV monochalcogenides, $MX$ ($M\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}\mathrm{Si}$, Ge, Sn, and Pb; $X\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}\mathrm{S}$, Se, and Te), are found to be either in a black phosphorene-derived distorted NaCl-type ($d$-NaCl) structure or a recently predicted $Pma2$ structure. Both $M$ and $X$ atoms in the $d$-NaCl structure are threefold coordinated, whereas $M$ and $X$ in the $Pma2$ structure are fourfold and twofold coordinated, respectively. Using first-principles total energy and electronic structure calculations and a global structural search technique, we systematically investigated the mechanism underlying the polymorphism of the 2D group-IV monochalcogenides. Our analysis show that the relative stability of the two distinct crystallographic phases depends on the strength of the $M\ensuremath{-}M$ covalent bond and the electronegativity difference between the constituent elements $M$ and $X$. For small cations, the covalency plays more important role, whereas for large cations the Coulomb interaction becomes more dominant. Therefore, the $\mathrm{Si}X$ and $\mathrm{Ge}X$ compounds assume the $Pma2$ structure, whereas the $MX$ compounds with heavy cation elements ($M\phantom{\rule{0.28em}{0ex}}=\phantom{\rule{0.28em}{0ex}}\mathrm{Sn}$ and Pb) tend to adopt the $d$-NaCl structure.