Valley splitting of monolayer Hf₃C₂O₂ by the spin–orbit coupling effect: first principles calculations using the HSE06 methods

Electrons have not only charge and spin degrees of freedom, but also additional valley degrees of freedom. The search for valleytronic materials with large valley splits is important for the development of valleytronics. In this work, we applied first principles computations to calculate 1 L Hf₃C₂O₂ at the level of HSE06. When the spin-orbit coupling (SOC) effect is considered, 1 L Hf₃C₂O₂ is an indirect bandgap semiconductor with a bandgap of 0.952 eV. Meanwhile, valley splitting occurs between the conduction bands Γ and K, with a valley splitting value as high as 98.228 meV. Bader charge analysis was used to determine that Hf-O and Hf-C are ionic bonds. The computed elastic constants and phonon spectra proved that 1 L Hf₃C₂O₂ is mechanically and dynamically stable. In addition, the Berry curvature of 1 L Hf₃C₂O₂ is non-zero. In the work the effect of the electronic properties of 1 L Hf₃C₂O₂ was also calculated with respect to the biaxial strain. The results show that the biaxial strain can well regulate the band gap and valley splitting. Finally, we calculated the effects of hole and electron doping on the band gap and valley splitting of 1 L Hf₃C₂O₂. The results show that the band gap and valley splitting are linearly related to the doping concentration. Our study shows that 1 L Hf₃C₂O₂ is a promising two-dimensional valleytronics material.