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Strain induced $\mathbb{Z}_2$ topological insulating state of $β$-As$_2$Te$_3$

Topological insulators are non-trivial quantum states of matter which exhibit a gap in the electronic structure of their bulk form, but a gapless metallic electronic spectrum at the surface. Here, we predict a uniaxial strain induced electronic topological transition (ETT) from a band to topological insulating state in the rhombohedral phase (space group: R$\bar{3}$m) of As$_2$Te$_3$ ($β$-As$_2$Te$_3$) through \textit{first-principles} calculations including spin-orbit coupling within density functional theory. The ETT in $β$-As$_2$Te$_3$ is shown to occur at the uniaxial strain $ε_{zz}$ = -0.05 ($σ_{zz}$=1.77 GPa), passing through a Weyl metallic state with a single Dirac cone in its electronic structure at the $Γ$ point. We demonstrate the ETT through band inversion and reversal of parity of the top of the valence and bottom of the conduction bands leading to change in the $\mathbb{Z}_2$ topological invariant $ν_0$ from 0 to 1 across the transition. Based on its electronic structure and phonon dispersion, we propose ultra-thin films of As$_2$Te$_3$ to be promising for use in ultra-thin stress sensors, charge pumps and thermoelectrics.