Topological phases protected by point group symmetry

Understand

We consider symmetry protected topological (SPT) phases with crystalline point group symmetry, dubbed point group SPT (pgSPT) phases.

• We show that such phases can be understood in terms of lower-dimensional topological phases with on-site symmetry, and can be constructed as stacks and arrays of these lower-dimensional states.
• This provides the basis for a general framework to classify and characterize bosonic and fermionic pgSPT phases, that can be applied for arbitrary crystalline point group symmetry and in arbitrary spatial dimension.
• We develop and illustrate this framework by means of a few examples, focusing on three-dimensional states.