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Topological nontrivial nature are the latest phases to be discovered incondensed matter physics with insulating bulk band gaps and topologicallyprotected metallic surface states; they are one of the current hot topicsbecause of their unique properties and potential applications. In this paper,we have highlighted a first-principles study of the structural stability andelectronic behavior of the Na${}_{2}$AgX (X= As, Sb and Bi) full Heuslercompounds, using the Full-Potential Linear Muffin-Tin Orbital (FP-LMTO) method.We have originated that the Hg${}_{2}$CuTi structure is appropriate in allstudied materials. The negative values of the calculated formation energiesmean that these compounds are energetically stable. The band structure isstudied for the two cases relating the existence and the absence ofspin-orbital couplings, where all materials are shown to be topologicallynon-trivial compounds. Spin orbital couplings were noticed to have nosignificant effect on the electronic properties such as the topological order.

A first-principles investigation of band inversion in topologically nontrivial Na2AgX (X= As, Sb and Bi) full Heusler compounds