Invariants for (2+1)D bosonic crystalline topological insulators for all 17 wallpaper groups

Vladimir Calvera, Naren Manjunath, Maissam Barkeshli

We study bosonic symmetry-protected topological (SPT) phases in (2+1) dimensions with symmetry $G=G_{\text{space}}\times K$, where $G_{\text{space}}$ is a general wallpaper group…