A coupled wire model of topological Weyl and Dirac fermion II: three-dimensional geometric topological phase

We mimic Weyl and Dirac semimetals in three dimensions by a coupled Dirac wire model, and introduce many-body gapping interactions that preserve symmetries. The construction relies on additional layers of gapped symmetric interacting surfaces of topological insulators, each carrying fractional charge excitations and containing Ising-like surface topological order. The three dimensional stack supports mutually non-local fractional point charges and flux tubes. Moreover the flux tubes, when directed in an appropriate direction, can carry Majorana zero modes and give rise to non-Abelian "3-loop braiding". Due to the highly anisotropic nature of the coupled wire model, the topological phase also exhibits geometric properties beyond a topological field theory description.