Hybrid-Functional and Quasi-Particle Calculations of Band Structures of Mg₂Si, Mg₂Ge, and Mg₂Sn

We perform hybrid functional and quasi-particle band structure calculations with spin-orbit interaction to investigate the band structures of Mg₂Si, Mg₂Ge, and Mg₂Sn. For all Mg₂X materials, where X = Si, Ge, and Sn, the characteristics of band edge states, i.e., band and valley degeneracies, and orbital characters, are found to be conserved, independent of the computational schemes such as density functional generalized gradient approximation, hybrid functionals, or quasi-particle calculations. However, the magnitude of the calculated band gap varies significantly with the computational schemes. Within density-functional calculations, the one-particle band gaps of Mg₂Si, Mg₂Ge, and Mg₂Sn are 0.191, 0.090, and −0.346 eV, respectively, and thus severely underestimated compared to the experimental gaps, due to the band gap error in the density functional theory and the significant relativistic effect on the low-energy band structures. By employing hybrid-functional calculations with a 35% fraction of the exact Hartree-Fock exchange energy (HSE-35%), we overcame the negative band gap issue in Mg₂Sn. Finally, in quasi-particle calculations on top of the HSE-35% Hamiltonians, we obtained band gaps of 0.835, 0.759, and 0.244 eV for Mg₂Si, Mg₂Ge, and Mg₂Sn, respectively, consistent with the experimental band gaps of 0.77, 0.74, and 0.36 eV, respectively.