Dirac crossings and band inversion in hexagonal superconductors emerging by chemical substitution: SrAlGe, BaAlGe, SrGaGe and BaGaGe

In this work, we used DFT calculations to compare the electronic structure of four hexagonal superconducting materials. Two of them are SrAlGe and BaAlGe, and the other two are given by substituting Al for Ga, resulting in SrGaGe and BaGaGe. The band structure, the density of states, and the Fermi surface were obtained for each compound with and without the spin–orbit coupling effect. For the SrGaGe and BaGaGe compounds, a band unfolding calculation was performed. We found that BaGaGe exhibits a quasi-flat-band localized in a specific direction of the Brillouin zone. In addition, band inversion can be induced by replacing Al for Ga in these compounds. Furthermore, we found that linear band crossings are gaped after spin–orbit coupling is considered to SrAlGe, BaAlGe, SrGaGe, and BaGaGe. These Dirac-like band crossings point to non-trivial topological behavior.