Multicellularity of delicate topological insulators

Abstract

Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the method of symmetry-based indicators. Despite having a symmetric, exponentially-localized Wannier representation, each Wannier function cannot be completely localized to a single primitive unit cell in the bulk. Such multicellular topology is shown to be neither stable, nor fragile, but delicate, i.e., the topology can be nullified by adding trivial bands to either valence or conduction band.

arXiv comment5 pages, 4 figures + supplemental material: 22 pages, 4 figures. Version 3: accepted version of the paper. New in main text: figures 1,2; minor improvements of the arguments. New in SM: comparison of multicellular topology and obstructed atomic insulators, proof that RTP implies multicellularity; non-analyticity of polarization; list of hexagonal magnetic space groups that support RTP

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