Topological order in interacting semimetals

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