## Speaker

## Details

The interplay between symmetry and topology allows a rich variety of electronic phases. For layered systems, symmetry under translation by one layer protects the 3D weak topological insulator, which can be viewed as a stack of 2D topological insulators and the 2D 'weak topological superconductor', which is a stack of 1D topological superconductors. In this talk we will explore related translation symmetry enriched states with strong interactions. We introduce a class of Abelian fractional quantum Hall states that have a translation symmetry enriched topological order that features a marriage of the Laughlin state and the toric code, for which translation symmetry acts as an anyonic symmetry. Such states have a natural description within the coupled wire construction, which establishes the connection between this type of topological order and non-diagonal conformal field theories. These states are also closely related to the weak topological superconductor, as well as a novel symmetry enriched insulating toric code phase. We will close with speculations on physical systems where such states might arise.