Exciton states of HfO₂ and Janus HfSO monolayers: first-principles investigations

In this work, we perform first-principles calculations to study the electronic and optical properties of HfO₂ and its Janus HfSO monolayers, with a particular emphasis on electron-hole interaction (excitonic effects). The electronic properties are investigated using a hierarchy of theoretical approaches, including standard density functional theory DFT (PBE), DFT (PBE)+U, DFT (PBE)+SOC, the hybrid functional DFT (HSE06), and many-body perturbation theory within the GW approximation. Both HfO₂ and HfSO monolayers are indirect-gap semiconductors, and the predicted band gaps increase as we apply more advanced levels of theory. We also examine electronic properties through complex orbital hybridization. Furthermore, we observed strongly bound excitonic states in both materials, including both optically active (bright) and inactive (dark) excitons, highlighting the significant role of excitonic effects. The pronounced excitonic effects identified in both materials suggest their potential for next-generation two-dimensional (2D) optoelectronic and photonic applications.