Anisotropic thermal expansion and thermodynamic properties of monolayer β -Te

Recently, β-Te [atomically two-dimensional (2D) tellurium] with rectangular crystal structure has been synthesized successfully on highly oriented pyrolytic graphite substrates by using molecular beam epitaxy [Z. Zhu, Phys. Rev. Lett. 119, 106101 (2017)10.1103/PhysRevLett.119.106101; Chen, Nanoscale 9, 15945 (2017)10.1039/C7NR04085G]. It has been found to possess remarkable properties such as ultralow lattice thermal conductivity and high thermoelectric efficiency. Based on first-principles calculations, we study the thermal expansion and thermodynamic properties of the experimental phase monolayer β-Te, using the quasiharmonic approach. It is found that β-Te shows large positive thermal expansion at elevated temperature, while the linear thermal expansion coefficient is negative along the a direction at very low temperature. The linear thermal expansion coefficient along the b direction is 4.9×10-5K-1 at 500 K, which is considerably large in 2D materials. β-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 Grüneisen parameters.