Stability of multinode Dirac semimetals against strong long-range correlations

We study the stability of Dirac semimetals with $N$ nodes in three spatial dimensions against strong $1/r$ long-range Coulomb interactions. We particularly study the cases of $N=4$ and $N=16$, where the $N=4$ Dirac semimetal is described by the staggered fermions and the $N=16$ Dirac semimetal is described by the doubled lattice fermions. We take into account the $1/r$ long-range Coulomb interactions between the bulk electrons. Based on the U(1) lattice gauge theory, we analyze the system from the strong coupling limit. It is shown that the Dirac semimetals survive in the strong coupling limit when the out-of-plane Fermi velocity anisotropy of the Dirac cones is weak, whereas they change to Mott insulators when the anisotropy is strong. A possible global phase diagram of correlated multinode Dirac semimetals is presented. Implications of our result to the stability of Weyl semimetals and three-dimensional topological insulators are discussed.

Figure 1

Fermi velocity anisotropy $v_{\mathrm{F}\perp }/v_{\mathrm{F}\parallel }$ dependence of the chiral condensate $\sigma$ for the $N=4$ case in the strong coupling limit $\left(\beta =0\right)$. When $v_{\mathrm{F}\perp }/v_{\mathrm{F}\parallel }=0$, the system corresponds to monolayer graphene in the strong coupling limit.

Figure 2

A possible global phase diagram of a correlated $N$-node Dirac semimetal with $N=4$. The $\beta =0 \left(\beta =\infty \right)$ line represents the strong coupling limit (noninteracting limit). The Mott insulator phase is defined as the phase with nonzero value of $\sigma$.