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We perform hybrid functional and quasi-particle band structure calculationswith spin-orbit interaction to investigate the band structures of Mg2Si, Mg2Ge,and Mg2Sn. For all Mg2X materials, where X = Si, Ge, and Sn, thecharacteristics of band edge states, i.e., band and valley degeneracies, andorbital characters, are found to be conserved, independent of the computationalschemes such as density functional generalized gradient approximation, hybridfunctionals, or quasi-particle calculations. However, the magnitude of thecalculated band gap varies significantly with the computational schemes. Withindensity-functional calculations, the one-particle band gaps of Mg2Si, Mg2Ge,and Mg2Sn are 0.191, 0.090, and -0.346 eV, respectively, and thus severelyunderestimated compared to the experimental gaps, due to the band gap error inthe density functional theory and the significant relativistic effect on thelow-energy band structures. By employing hybrid-functional calculations with a35% fraction of the exact Hartree-Fock exchange energy (HSE-35%), we overcamethe negative band gap issue in Mg2Sn. Finally, in quasi-particle calculationson top of the HSE-35% Hamiltonians, we obtained band gaps of 0.835, 0.759, and0.244 eV for Mg2Si, Mg2Ge, and Mg2Sn, respectively, consistent with theexperimental band gaps of 0.77, 0.74, and 0.36 eV, respectively.

Hybrid-functional and quasi-particle calculations of band structures of Mg2Si, Mg2Ge, and Mg2Sn