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The bi-alkali pnictogens have attracted significant attention foroptoelectronic and photocathodic device applications. However, in most of thecompounds belonging to this family, there has been less effort put intoinvestigating the mechanical properties and topological phase transitions (TPT)of the compounds. Here, in the framework of density functional theory, themechanical properties and topological phase transition of NaLi$_{2}$Bi underhydrostatic pressures are investigated. Elastic constants and phononcalculations have shown the mechanical and dynamical stability of this compoundunder hydrostatic tension and compression. The analysis of the elasticconstants shows that the NaLi$_{2}$Bi in the equilibrium state is an auxeticmaterial with a negative Poisson's ratio of -0.285, which changes to a materialwith a positive Poisson's ratio under hydrostatic tension. Meanwhile, Poisson'sratio and Pugh ratio indicate that this compound has brittle behavior andmaintains it under hydrostatic pressures. The calculated results of the bandstructure within the generalized gradient approximation (GGA) (Tran-Blahamodified Becke-Johnson exchange potential approximation (TB-mBJ)) show thatNaLi$_{2}$Bi is a nontrivial topological material (trivial topologicalmaterial). It was found that hydrostatic compression (tension) in the GGA(TB-mBJ) approach leads to a transition from a nontrivial (trivial) to atrivial (nontrivial) topological phase for this compound. Moreover, thecalculated Wannier charge centers confirm the TPT. Identifying the mechanismscontrolling the auxetic behavior and TPT of this compound offers a valuablefeature for designing and developing high-performance nanoscaleelectromechanical and spintronic devices.

Effect of hydrostatic strain on the mechanical properties and topological phase transition of bi-alkali pnictogen NaLi$_{2}$Bi