Condensed Matter Zoom Seminar | Charles Kane, U Penn.| "Translation symmetry enriched topological phases"

Wed, Apr 7, 2021, 2:00 pm

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.