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We study the excitonic semimetal-insulator quantum phase transition inthree-dimensional Dirac semimetal in which the fermion dispersion is stronglyanisotropic. After solving the Dyson-Schwinger equation for the excitonic gap,we obtain a global phase diagram in the plane spanned by the parameter forCoulomb interaction strength and the parameter for fermion velocity anisotropy.We find that excitonic gap generation is promoted as the interaction becomesstronger, but is suppressed if the anisotropy increases. Applying our resultsto two realistic three-dimensional Dirac semimetals Na$_{3}$Bi andCd$_{3}$As$_{2}$, we establish that their exact zero-temperature ground stateis gapless semimetal, rather than excitonic insulator. Moreover, these twomaterials are far from the excitonic quantum critical point, thus there shouldnot be any observable evidence for excitonic insulating behavior. Thisconclusion is in general agreement with the existing experiments of Na$_{3}$Biand Cd$_{3}$As$_{2}$.

Robustness of the semimetal state of Na3Bi and Cd3As2 against Coulomb interaction