How much topological insulation does one need? how much can one get?

Topological insulators (TIs) have taken electromagnetic-engineering research by a storm this decade, and numerous theoretical papers have been published after modeling a TI as a nonreciprocal biisotropic material. As the TI phenomenon macroscopically is manifested only at boundaries, the assumed nonreciprocity in the bulk is fallacious. The TI phenomenon is better accommodated as a boundary condition indicating the presence of conducting states of a specific type. Theory shows that the TI effects in the free space surrounding a region occupied by a TI material do not depend on the specific model chosen. We have collectively examined frequency-domain scattering by planar surfaces, TI-coated gratings, and spheres in order to answer the first question in the title of this presentation. Our answer is: a lot. Based on a review of experimental data available on a variety of chalcogenide TIs, our answer to the second question in the title of this presentation is: much less.