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

TL;DR

This study uses hybrid functional and quasi-particle calculations to accurately determine the band structures and gaps of Mg2Si, Mg2Ge, and Mg2Sn, aligning well with experimental data and highlighting the importance of computational scheme choice.

Contribution

It demonstrates the effectiveness of hybrid and quasi-particle methods in accurately predicting the electronic properties of Mg2X materials, improving upon standard density functional results.

Findings

Band edge characteristics are conserved across computational schemes.

Standard DFT significantly underestimates band gaps.

Quasi-particle calculations yield band gaps consistent with experiments.

Abstract

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.