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Density functional theory (DFT) approaches have been ubiquitously used topredict topological order and non-trivial band crossings in real materials,like Dirac, Weyl semimetals and so on. However, use of less accurateexchange-correlation functional often yields false prediction of non-trivialband order leading to misguide the experimental judgment about such materials.Using relatively more accurate hybrid functional exchange-correlation, weexplore a set of (already) experimentally synthesized materials (crystallizingin space group P6_3/mmc) Our calculations based on more accurate functionalhelps to correct various previous predictions for this material class. Based onpoint group symmetry analysis and ab-initio calculations, we systematicallyshow how lattice symmetry breaking via alloy engineering manifests differentfermionic behavior, namely Dirac, triple point and Weyl in a single material.Out of various compounds, XAgBi (X=Ba,Sr) turn out to be two ideal candidates,in which the topological nodal point lie very close to the Fermi level, withinminimal/no extra Fermi pocket. We further studied the surface states and Fermiarc topology on the surface of Dirac, triple point and Weyl semimetallic phasesof BaAgBi. We firmly believe that, while the crystal symmetry is essential toprotect the band crossings, the use of accurate exchange correlation functionalin any DFT calculation is an important necessity for correct prediction of bandorder which can be trusted and explored in future experiments.

Symmetry driven topological phases in XAgBi (X=Ba,Sr): An Ab-initio hybrid functional calculations