First-principles insights into the thermodynamically stable 1T-HfSn₂N₄ monolayer

Abstract Recently, the layered MA 2 Z 4 family of 2D materials, composed of transition metals (M), group-IV elements (A), and group-V pnictogens (Z), have drawn increasing attention due to their diverse structural configurations and tunable optoelectronic properties. In this work, we employ first-principles density functional theory (DFT) simulations to systematically examine the structural stability of HfSn 2 N 4 monolayer in both the 1T and 2H phases. Our results show that the 2H phase is not only energetically less favorable but also dynamically unstable, as indicated by total ground state energy and the presence of imaginary phonon modes. Conversly, the 1T phase due to octahedral coordination of Hf atom exhibits both the ground state and thermodynamic stability, suggesting its experimental realizability. The computed elastic constants reveal a Young’s modulus of 321.27 N/m and a Poisson’s ratio of 0.25 for 1T-HfSn 2 N 4 , which are significantly higher than those typically observed in other binary 2D systems, and satisfy the Born criterion for mechanical stability. Electronic structure calculations based on PBE and HSE06 functionals confirm that the HfSn 2 N 4 monolayer possesses a direct bandgap semiconductor, with the bandgap increasing from 0.55 eV (PBE) to 1.71 eV (HSE06). Optical absorption spectra further confirm strong light–matter interaction, indicating potential use in IR photodetectors, terahertz (THz) sensing technologies and optoelectronics. Notably, the electronic and optical characteristics of HfSn 2 N 4 monolayer can be efficiently tuned via biaxial strain engineering, enabling controlled tuning of the bandgap and optical response. These findings establish the HfSn 2 N 4 monolayer as a compelling material for use in flexible nanoscale and optoelectronic applications.