Anisotropic thermal expansion and thermomechanic properties of monolayer β-Te

Recently, $\beta$-Te (atomically 2D tellurium) with rectangular crystal structure has been synthesized successfully on highly oriented pyrolytic graphite substrates by using molecular beam epitaxy. It has been found possessing remarkable properties such as ultralow lattice thermal conductivity and high thermoelectric efficiency. Based on the first-principles calculations, we study the thermal expansion and thermomechanic properties of the experimental phase monolayer $\beta$-Te, using quasiharmonic approach. It is found $\beta$-Te shows large positive thermal expansion at elevated temperature, while the linear thermal expansion coefficient is negative along a direction at very low temperature. The linear thermal expansion coefficient along b direction is 4.9*10$^{-5}$ K$^{-1}$ at 500 K, which is considerably large in 2D materials. $\beta$-Te exhibits strong in-plane anisotropy, including thermal expansion, 2D elastic moduli and Poisson's ratios. However, the elastic moduli, Poisson's ratios and the in-plane anisotropy are weakened with increasing temperature, and the variations are dominated by the generalized mode Gr\"{u}neisen parameters.