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By means of first-principles calculations, we identified the structural phasetransition of Na$_3$Bi from hexagonal ground state to cubic $cF$16 phase above0.8 GPa, in agreement with the experimental findings. Upon the releasing ofpressure, \emph{cF}16 phase of Na$_3$Bi is mechanically stable at ambientcondition. The calculations revealed that the $cF$16 phase is topologicalsemimetal, in similarity to well-known HgTe and it even exhibits an unusuallylow $C^\prime$ modulus (only about 1.9 GPa) and a huge anisotropy, $A^u$ of ashigh as 11, the third highest value among all known cubic crystals in theirelastic behaviors. These facts render \emph{cF}16-type Na$_3$Bi very soft witha liquid-like elastic deformation in the (110)$<$1$\overline{1}$0$>$ slipsystem. Importantly, as accompanied with this deformation, Na$_3$Bi shows atopological phase transition from a topological semimetal state at itsstrain-free cubic phase to a topological insulating state at its distortedphase. Because the $C^\prime$ elastic deformation almost costs no energy in areversible and liquid-like soft manner, \emph{cF}16-type Na$_3$Bi wouldpotentially provide a fast on/off switching way between topological insulatorand topological semimetal, which would be beneficial to the quantum electronicdevices for practical applications.

Combined Fast Reversible Liquid-like Elastic Deformation with Topological Phase Transition in Na$_3$Bi