From Dirac semimetals to topological phases in three dimensions: a coupled wire construction

TL;DR

This paper explores how strong many-body interactions in three-dimensional Dirac and Weyl semimetals can induce new topological phases and gaps without breaking symmetries, revealing fractionalized excitations and boundary phenomena.

Contribution

It introduces a coupled wire construction to demonstrate interaction-driven topological phases in 3D Dirac/Weyl semimetals beyond mean-field theory.

Findings

Dirac semimetals can acquire a many-body gap preserving symmetries.

Interactions enable anomalous Weyl phases forbidden in single-body models.

Both phases support fractionalized bulk and boundary quasiparticles.

Abstract

Weyl and Dirac (semi)metals in three dimensions have robust gapless electronic band structures. Their massless single-body energy spectra are protected by symmetries such as lattice translation, (screw) rotation and time reversal. In this manuscript, we discuss many-body interactions in these systems. We focus on strong interactions that preserve symmetries and are outside the single-body mean-field regime. By mapping a Dirac (semi)metal to a model based on a three dimensional array of coupled Dirac wires, we show (1) the Dirac (semi)metal can acquire a many-body excitation energy gap without breaking the relevant symmetries, and (2) interaction can enable an anomalous Weyl (semi)metallic phase that is otherwise forbidden by symmetries in the single-body setting and can only be present holographically on the boundary of a four dimensional weak topological insulator. Both of these topological states support fractional gapped (gapless) bulk (resp. boundary) quasiparticle excitations.