Multicellularity of delicate topological insulators

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.

对于拓扑绝缘体而言，仅具有可万尼尔化的特性并非故事的终结。本研究引入了一类拓扑绝缘体，在十重法、拓扑量子化学以及基于对称性的指示方法所构建的范式下，此类绝缘体将被视为平凡。尽管这些绝缘体具有对称的、指数级局部化的万尼尔表示，但每个万尼尔函数并不能完全局限于宏观晶体中的单个基本单元。这种多细胞拓扑结构被证明既非稳定亦非脆弱，而是脆弱的；即，通过向价带或导带添加平凡能带，即可消除这种拓扑。