Theoretical Study of The Electronic Properties of a 3D Dirac Semimetal Ge₄Sn using First-principles

A recent theoretical study¹ has predicted the topological nature of two materials with tetragonal structures: Ge₅ and Sn₅. Building upon this research, we investigated the electronic properties of Ge₄Sn, which shares a similar crystal structure. Our study shows that Ge₄Sn is metallic and non-magnetic in nature. Notably, the lattice parameters of Ge₄Sn are somewhat larger than those of Ge₅, yet significantly smaller than Sn₅. This discrepancy can be attributed to the relatively smaller size of the Ge atom in comparison to Sn. The chemical bonds of Ge₄Sn have covalent characteristics confirmed by the charge density plot. Furthermore, we find a strong hybridization between Ge 4<i>p </i>and Sn 5<i>p </i>orbitals in the energy range −4 to 0 eV below the Fermi energy. The highly anisotropic Dirac cone appears near<i> the A</i> point in the band structure without spin-orbit interaction. However, the inclusion of spin-orbit interaction leads to a significant band-splitting around <i>A</i> point as well. Topological properties are studied by calculating topological invariant and surface states. These results collectively demonstrate that Ge₄Sn exhibits the characteristics of a 3D Dirac semimetal. Further study is needed to uncover novel properties of Ge₄Sn.<br/>[1] C. Zhong, Front. Phys. <b>16(6)</b>, 63503 (2021).