Multicellularity of delicate topological insulators

TL;DR

This paper introduces a new class of topological insulators with Wannier representations that are symmetric and localized but cannot be confined to a single unit cell, revealing a delicate form of topology that can be nullified by trivial bands.

Contribution

It presents the concept of multicellular topology in topological insulators, expanding the understanding beyond existing classification schemes.

Findings

Wannier functions cannot be localized to a single unit cell

Multicellular topology can be nullified by adding trivial bands

The topology is neither stable nor fragile, but delicate.

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.