A First-Principles Study of Nonlinear Elastic Behavior and Anisotropic Electronic Properties of Two-Dimensional HfS₂

We utilize first principles calculations to investigate the mechanical properties and strain-dependent electronic band structure of the hexagonal phase of two dimensional (2D) HfS₂. We apply three different deformation modes within -10% to 30% range of two uniaxial (D1, D2) and one biaxial (D3) strains along x, y, and x-y directions, respectively. The harmonic regions are identified in each deformation mode. The ultimate stress for D1, D2, and D3 deformations is obtained as 0.037, 0.038 and 0.044 (eV/Ang3), respectively. Additionally, the ultimate strain for D1, D2, and D3 deformation is obtained as 17.2, 17.51, and 21.17 (eV/Ang3), respectively. In the next step, we determine the second-, third-, and fourth-order elastic constants and the electronic properties of both unstrained and strained HfS₂ monolayers are investigated. Our findings reveal that the unstrained HfS₂ monolayer is a semiconductor with an indirect bandgap of 1.12 eV. We then tune the bandgap of HfS₂ with strain engineering. Our findings reveal how to tune and control the electronic properties of HfS₂ monolayer with strain engineering, and make it a potential candidate for a wide range of applications including photovoltaics, electronics and optoelectronics.