Density functional theory (DFT) approaches have been ubiquitously used to predict topological order and nontrivial band crossings in real materials, like Dirac, Weyl semimetals, and so on. However, the use of less accurate exchange-correlation functional often yields a false prediction of nontrivial band order leading to misguide the experimental judgment about such materials. Using relatively more accurate hybrid functional exchange correlation, we explore a set of (already) experimentally synthesized materials (crystallizing in space group $P{6}_3/mmc$). Our calculations based on more accurate functional helps to correct various previous predictions for this material class. Based on point group symmetry analysis and ab initio calculations, we systematically show how lattice symmetry breaking via alloy engineering manifests different fermionic behavior, namely, Dirac, triple point, and Weyl in a single material. Out of various compounds, $X\mathrm{AgBi}$ ($X$=Ba,Sr) turns out to be two ideal candidates, in which the topological nodal point lies very close to the Fermi level, within minimal/no extra Fermi pocket. We further studied the surface states and Fermi arc topology on the surface of Dirac, triple point, and Weyl semimetallic phases of BaAgBi. We firmly believe that, while the crystal symmetry is essential to protect the band crossings, the use of accurate exchange correlation functional in any DFT calculation is an important necessity for the correct prediction of band order which can be trusted and explored in future experiments.

• Received 26 February 2020
• Revised 28 June 2020
• Accepted 27 July 2020

DOI:https://doi.org/10.1103/PhysRevMaterials.4.084201