We present a prediction of the Dirac semimetal (DSM) phase in ${\mathrm{MgTa}}_2{\mathrm{N}}_3$ based on first-principles calculations and a symmetry analysis. In this material, the Fermi level is located exactly at the Dirac point without additional Fermi surface pockets. The band inversion associated with the Dirac cone involves the $d$ orbitals of two structurally inequivalent Ta atoms with octahedral and trigonal prismatic coordination spheres. We further show that the lattice symmetry breaking can realize topological phase transitions from the DSM phase to a triple nodal point semimetal, Weyl semimetal, or topological insulator. The topologically protected surface states and the nonprotected Fermi arc surface states are also studied.

• Received 16 May 2018

DOI:https://doi.org/10.1103/PhysRevB.98.081115