Broken symmetry driven phase transitions from a topological semimetal to a gapped topological phase in SrAgAs

We show the occurrence of Dirac, triple-point, Weyl semimetal, and topological insulating phases in a single ternary compound using specific symmetry-preserving perturbations. Based on first-principles calculations, the $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ model, and symmetry analysis, we show that alloying-induced precise symmetry breaking in SrAgAs (space group $\mathrm{P}{6}_{3}/mmc$) leads us to tune various low-energy excitonic phases transforming from Dirac to topological insulating via the intermediate triple-point and Weyl semimetal phases. We also consider the effect of external magnetic field, causing time reversal symmetry (TRS) breaking and analyze the effect of TRS on the realization of the Weyl state. Importantly, in this material, the Fermi level lies extremely close to the nodal point with no extra Fermi pockets, which further makes this compound an ideal platform for topological study. The multifold band degeneracies in these topological phases are analyzed based on point group representation theory. The topological insulating phase is further confirmed by calculating the ${\mathrm{Z}}_{2}$ index. Furthermore, the topologically protected surface states and Fermi arcs are investigated in some detail.