Strain can be used as an effective tool to tune the crystal structure of materials and hence to modify their electronic structures, including topological properties. Here, taking ${\mathrm{Na}}_3\mathrm{Bi}$ as a paradigmatic example, we demonstrated with first-principles calculations and $\mathbf{k}·\mathbf{p}$ models that the topological phase transitions can be induced by various types of strains. For instance, the Dirac semimetal phase of ambient ${\mathrm{Na}}_3\mathrm{Bi}$ can be tuned into a topological insulator (TI) phase by uniaxial strain along the $\langle 100\rangle$ axis. Hydrostatic pressure can let the ambient structure transfer into a new thermodynamically stable phase with $Fm\overline{3}m$ symmetry, coming with a perfect parabolic semimetal having a single contact point between the conduction and valence bands, exactly at the $\mathrm{\Gamma }$ point on the Fermi surface, similar to $\alpha$-Sn. Furthermore, uniaxial strain in the $\langle 100\rangle$ direction can tune the new parabolic semimetal phase into a Dirac semimetal, while shear strains in both the $\langle 100\rangle$ and $\langle 111\rangle$ directions can take the new parabolic semimetal phase into a TI. $\mathbf{k}·\mathbf{p}$ models are constructed to gain more insights into these quantum topological phase transitions. Last, we calculated surface states of $Fm\overline{3}m{\mathrm{Na}}_3\mathrm{Bi}$ without and with strains to verify these topological transitions.

• Received 4 April 2017
• Revised 15 July 2017

DOI:https://doi.org/10.1103/PhysRevB.96.075112