MgXN₂ (X = Hf/Zr) Monolayers: Auxetic Semiconductor with Highly Anisotropic Optical/Mechanical Properties and Carrier Mobility

Two-dimensional (2D) semiconducting materials with distinct anisotropic physical properties have attracted intense interests. Herein, we show theoretical predictions that MgXN₂ (X = Hf/Zr) monolayers are auxetic semiconductors with highly anisotropic electronic, optical, and mechanical properties. The density functional theory calculations coupled with a PSO algorithm (global-minimum search) suggest that both MgHfN₂ (MgZrN₂) monolayers exhibit orthorhombic symmetry (Pmma) and are direct-gap (indirect-gap) semiconductors with a bandgap of 2.43 eV (2.13 eV). Specifically, the MgHfN₂ monolayer exhibits highly anisotropic hole mobility as well as very high electron mobility (~10⁴ cm² V^-1 s^-1). G₀W₀+BSE calculations indicate that both monolayers bear notable optical anisotropy and relatively large exitonic binding energy (~0.6 eV). In addition, both monolayers acquire remarkable mechanical anisotropy with a negative in-plane Poisson's ratio (~-0.2) and high Young's modulus (~260 N/m). The combination of highly anisotropic electronic, optical, and mechanical properties endows MgXN₂ monolayers as potentially useful parts in multifunctional nanoelectronic devices.