We study theoretically the electron correlation effect in a three-dimensional (3D) Dirac fermion system which describes a topologically nontrivial state. It is shown within the mean-field approximation that time-reversal and inversion symmetries of the system are spontaneously broken in the region where both spin-orbit coupling and electron correlation are strong. This phase is considered as a condensed-matter analog of the corresponding phase in the lattice quantum chromodynamics (QCD). It is also shown that in the presence of magnetic impurities, electron correlation enhances the appearance of the Weyl semimetal phase between the topological insulator phase and the normal insulator phase.
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