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.

5 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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• Real Hopf Insulator
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• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Homotopic classification of band structures: Stable, fragile, delicate, and stable representation-protected topology
• Protected Gapless Edge States In Trivial Topology
• Textured Exciton Insulators
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• Scattering theory of delicate topological insulators
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• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Flat Bands in Three-dimensional Lattice Models with Non-trivial Hopf Index
• Representation-protected topology of spin-singlet $s$-wave superconductors
• Hopf Semimetals
• Three-dimensional $\mathbb{Z}$ topological insulators without reflection symmetry
• Non-Hermitian Hopf insulators
• Superfluid stiffness of superconductors with delicate topology
• PT-symmetric Non-Hermitian Hopf Metal
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Correlated Hopf insulators