Thermally driven phase transitions in freestanding low-buckled silicene, germanene, and stanene

Abstract

Low-buckled silicene, germanene, and stanene are group-IV graphene allotropes. They form a honeycomb lattice out of two interpenetrating ($A$ and $B$) triangular sublattices that are vertically separated by a small distance ${\mathrm{\ensuremath{\Delta}}}_{z}$. The atomic numbers $Z$ of silicon, germanium, and tin are larger than that of carbon (${Z}_{\text{C}}=6$), making them the first experimentally viable two-dimensional topological insulators. Those materials have a twice-energy-degenerate atomistic structure characterized by the buckling direction of the $B$ sublattice with respect to the $A$ sublattice [whereby the $B$ atom either protrudes above (${\mathrm{\ensuremath{\Delta}}}_{z}>0$) or below (${\mathrm{\ensuremath{\Delta}}}_{z}<0$) the $A$ atoms], and the consequences of that energy degeneracy on their elastic and electronic properties have not been reported thus far. Here, we uncover ferroelastic, bistable behavior on silicene, which turns into an average planar structure at about 600 K. Furthermore, the creation of electron and hole puddles obfuscates the zero-temperature spin-orbit coupling (SOC)-induced band gaps at temperatures as low as 200 K, which may discard silicene as a viable two-dimensional topological insulator for room-temperature applications. Germanene, on the other hand, never undergoes a low-buckled-to-planar two-dimensional transformation, becoming amorphous at around 675 K instead, and preserving its SOC-induced band gap despite band broadening. Stanene undergoes a transition onto a crystalline three-dimensional structure at about 300 K, preserving its SOC-induced electronic band gap up to that temperature. Unlike what is observed in silicene and germanene, stanene readily develops a higher-coordinated structure with a high degree of structural order. The structural phenomena are shown to have far-reaching consequences for the electronic and vibrational properties of those two-dimensional topological insulators.