An antiferromagnetic semimetal has been recently identified as a new member
of topological semimetals that may host three-dimensional symmetry-protected
Dirac fermions. A reorientation of the N\'{e}el vector may break the underlying
symmetry and open a gap in the quasi-particle spectrum, inducing the
(semi)metal-insulator transition. Here, we predict that such transition may be
controlled by manipulating the chemical potential location of the material. We
perform both analytical and numerical analysis on the thermodynamic potential
of the model Hamiltonian and find that the gapped spectrum is preferred when
the chemical potential is located at the Dirac point. As the chemical potential
deviates from the Dirac point, the system shows a possible transition from the
gapped to the gapless phase and switches the corresponding N\'{e}el vector
configuration. We perform density functional theory calculations to verify our
analysis using a realistic material and discuss a two terminal transport
measurement as a possible route to identify the voltage induced switching of
the N\'{e}el vector.Comment: 16 pages, 9 figures, the density functional theory calculation
analysis (Section IV.D) has been modifie