Composite Weyl semimetal as a parent state for three-dimensional topologically ordered phases

We introduce $(3+1)$-dimensional models of short-range-interacting electrons that form a strongly correlated many-body state whose low-energy excitations are relativistic neutral fermions coupled to an emergent gauge field, ${\text{QED}}_4$. We discuss the properties of this critical state and its instabilities towards exotic phases such as a gapless “composite” Weyl semimetal and fully gapped topologically ordered phases that feature anyonic pointlike as well as linelike excitations. These fractionalized phases describe electronic insulators. They may be further enriched by symmetries which result in the formation of nontrivial surface states.

Figure 1

A schematic depiction of the superlattice we study. The system is composed of alternating topological and normal insulators. Each interface contains a single Dirac cone, known to be dual to a ${\text{QED}}_3$ theory describing neutral fermions coupled to an emergent gauge field. We demonstrate that interactions can deconfine the neutral fermions, leading to a ${\text{QED}}_4$ theory, from which nontrivial three-dimensional phases descend.

Figure 2

The phase diagram describing the properties of the system as a function of the mass $m$ and the amplitude $\mathrm{\Delta }$ of the dual pairing terms. We show that the ${\text{QED}}_4$ theory serves as a parent state for the composite Weyl semimetal state and topologically ordered gapped phases. If the mass is large enough, the system becomes a thermal Hall insulator, with the dual fermions forming a band insulator which is adiabatically connectable to a stack of Chern insulators.