Topological order in interacting semimetals

TL;DR

This paper explores novel topologically ordered states in interacting semimetals, revealing a second fractional quantum Hall state with unique properties and implications for gapless phases and dualities in three dimensions.

Contribution

It identifies a second fractional quantum Hall state in interacting Weyl semimetals with the same Hall responses but distinct topological order, and discusses a topologically ordered state from gapped nodal line semimetals.

Findings

Existence of a second fractional quantum Hall state with fracton order.

Presence of a gapless phase with identical topological response to a Weyl semimetal.

Construction of a topologically ordered state from gapped nodal line semimetals.

Abstract

It has recently been demonstrated that it is possible to open a gap in a magnetic Weyl semimetal, while preserving the chiral anomaly along with the charge conservation and translational symmetries, which all protect the gapless nodes in a weakly interacting semimetal. The resulting state was shown to be a nontrivial generalization of a nonabelian fractional quantum Hall liquid to three dimensions. Here we point out that a second fractional quantum Hall state exists in this case. This state has exactly the same electrical and thermal Hall responses as the first, but a distinct (fracton) topological order. Moreover, the existence of this second fractional quantum Hall state necessarily implies a gapless phase, which has identical topological response to a noninteracting Weyl semimetal, but is distinct from it. This may be viewed as a generalization (in a weaker form) of the known duality between a noninteracting two-dimensional Dirac fermion and QED$_3$ to $3+1$ dimensions. In addition we discuss a $(3+1)$-dimensional topologically ordered state, obtained by gapping a nodal line semimetal without breaking symmetries.