Topological Properties of Insulators with Inversion Symmetry

There are many phases of insulators with inversion symmetry (with no other symmetry required). In particular, certain inversion parities cannot change unless there is a phase transition. I will show how to use these parities to classify phases of topological insulators and explain which combinations of these parities have physical consequences (e.g. for the magnetoelectric effect). Many of these results can be derived by pictorial arguments using the entanglement spectrum.