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arXiv · 2301.03628

Topological order in interacting semimetals

Jinmin Yi·Xuzhe Ying·Lei Gioia·A. A. Burkov
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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.

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Jinmin Yi, Xuzhe Ying, Lei Gioia, A. A. Burkov. 2023-03-24. Topological order in interacting semimetals. https://doi.org/10.1103/physrevb.107.115147

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