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

TL;DR

This paper investigates how Coulomb interactions and anisotropy affect the stability of the semimetal state in Na3Bi and Cd3As2, concluding they remain gapless and are not near excitonic insulator transitions.

Contribution

The study provides a phase diagram for 3D Dirac semimetals considering Coulomb interaction and anisotropy, showing these materials are stable semimetals.

Findings

Excitonic gap generation increases with stronger Coulomb interaction.

Higher anisotropy suppresses excitonic gap formation.

Na3Bi and Cd3As2 are far from excitonic quantum critical point.

Abstract

We study the excitonic semimetal-insulator quantum phase transition in three-dimensional Dirac semimetal in which the fermion dispersion is strongly anisotropic. After solving the Dyson-Schwinger equation for the excitonic gap, we obtain a global phase diagram in the plane spanned by the parameter for Coulomb interaction strength and the parameter for fermion velocity anisotropy. We find that excitonic gap generation is promoted as the interaction becomes stronger, but is suppressed if the anisotropy increases. Applying our results to two realistic three-dimensional Dirac semimetals Na$_{3}$Bi and Cd$_{3}$As$_{2}$, we establish that their exact zero-temperature ground state is gapless semimetal, rather than excitonic insulator. Moreover, these two materials are far from the excitonic quantum critical point, thus there should not be any observable evidence for excitonic insulating behavior. This conclusion is in general agreement with the existing experiments of Na$_{3}$Bi and Cd$_{3}$As$_{2}$.