Multicellularity of delicate topological insulators

We enrich the notions of stable and fragile topology by introducing delicate topological insulators: band structures possessing topological invariants that can be trivialized through an addition of a trivial conduction band. We find that although delicate topological insulators are Wannier representable with exponentially-localized symmetry-preserving Wannier functions, they can possess a different type of obstruction to an atomic limit. Namely, the impossibility to localize all Wannier functions to one unit cell, i.e. multicellularity.

In this talk, I will present two classes of tight-binding models that are both delicate and multicellular. The first is a 3D rotationally symmetric topological insulator which exhibits a returning Thouless pump, while the second is the Hopf insulator, both of which would be considered trivial under the commonly used classification methods such as symmetry indicators, topological quantum chemistry, and tenfold way. I will clarify how the respective topological invariants of these models lead to their multicellular and delicate character.

[1]. Nelson, A., Neupert, T., Bzdušek, T. & Alexandradinata, A. arXiv:2009.01863