Stability of Multinode Dirac Semimetals against Strong Long-Range Correlations

TL;DR

This study investigates the stability of multinode Dirac semimetals under strong Coulomb interactions, revealing that they remain stable with weak anisotropy but become Mott insulators when anisotropy is strong, with implications for related topological phases.

Contribution

The paper provides a lattice gauge theory analysis of multinode Dirac semimetals under strong long-range Coulomb interactions, highlighting the role of Fermi velocity anisotropy in their stability.

Findings

Dirac semimetals survive strong coupling with weak anisotropy.

Strong anisotropy leads to Mott insulator transition.

Global phase diagram for multinode Dirac semimetals is proposed.

Abstract

We study the stability of Dirac semimetals with $N$ nodes in three spatial dimensions against strong $1/r$ 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.