Hidden layered structures from carbon-analog metastability in metal dichalcogenides

Abstract

Carbon exhibits both a layered ground state structure that produces two-dimensional (2D) nanosheets and a non-layered diamond structure created under high pressure conditions. Motivated by this metastability relationship, we revisit the ground state structure of metal dichalcogenides that are known to have non-layered pyrite-type structure. Ultrathin films of pyrite-type ZnSe$_2$ spontaneously transform into a layered phase. This phase is identified as a ground state, and the monolayer exhibits strong elastic anisotropy and a semiconducting bandgap larger than that of the pyrite phase by a factor of two. We demonstrate that a two-valued but directional potential energy surface exists along a Bain-like distortion path, hiding the layered ground state. This work implies that many 2D materials are hidden in non-layered materials and connects 2D materials science with surface and high-pressure science.

Figures (3)

• Figure 1: (a) Schematic illustration of the potential energy surface. Carbon adopts a layered structure as the ground state and a non-layered structure as a metastable state. II-VI semiconductors adopt the pyrite-type structure synthesized under high pressure conditions, in turn, implying the existence of a hidden layered structure. (b) $\Delta E$ as a function of $N$ for thin films derived from the pyrite (001) surface. The dashed line indicates $\Delta E \propto N^{-1}$. The slab model calculations were not converged for $N\ge 7$ in CdTe$_2$ and $N\ge 8$ in ZnTe$_2$, but the layered phase is preferred in the bulk limit (see Fig. \ref{['fig3']}). (c) The side views of ZnSe$_2$ thin film structure up to $N=8$. $N=2$ thin film is terminated by Se atoms, serving as a building block for creating the vdW 2D ZnSe$_2$ with $N=4$-8. (d) The binding energy of $N=4$ ZnSe$_2$ and CdSe$_2$ as a function of the interlayer distance $d$ that is equal to the distance along the $z$ direction between Zn (Cd) atoms of different layers (see the inset). The rigid $N=2$ monolayer is assumed for "unrelax", and only the $z$ coordinates of Zn (Cd) pairs of different layers are fixed for "relax". The (12,6)-Lennard-Jones potential is used to fit the calculated data (filled circle).
• Figure 2: (a) Stress-strain curves of $N=2$ ZnSe$_2$ monolayer. (b) Evolution of the electron band structure for $N$ ZnSe$_2$ thin films (PBE-GGA). The band gap at $N=10$ is small because the thin film keeps the initial pyrite-type geometry. (c) The projected density-of-states of $N=2$ and 10 thin films. Energy is measured from the Fermi level.
• Figure 3: Bain-like distortion, with $a$ and $b$ axes relaxed for each $c$, staring from the layered ground state structure for (a) ZnSe$_2$ and (b) C. Once ZnSe$_2$ forms the pyrite-type phase, the strain energy $\delta E$ increases with $c$ through different energy path leading to the orthorhombic phase like PdSe$_2$oyedele2017. On the other hand, the layered phase recovers if a tensile strain along the [111] direction is applied to the diamond carbon. (c) $\Delta H$ in Eq. (\ref{['eq:enthalpy']}) of pyrite-type and layered phases. For CdSe$_2$, the layered structure relaxed to the pyrite-type phase.