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The three-dimensional topological Dirac semimetal Na$_3$Bi: the ground state phase

By means of first-principles calculations, we found that the early characterized three-dimensional topological bulk Dirac semimetal of the $P$6$_3$/$mmc$ Na$_3$Bi is dynamically unstable at the ground state due to the presence of the large imaginary phonon frequencies around the $K$ point. Alternatively, our calculations suggest a new ground state phase which crystalizes in the $P$$\overline3$$c$1 structure with a buckled graphite-like Na/Bi sheets, which is both energetically and dynamically more stable. Moreover, the calculations also uncovered that the $P$$\overline3$$c$1 phase at the ground state is also a topological 3D Dirac semimetal, being exactly the same as the electronic states of the metastable $P$6$_3$/$mmc$ phase.