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Multicellularity of delicate topological insulators

Aleksandra Nelson1*, Titus Neupert1, Tomáš Bzdušek2,1, Aris Alexandradinata3,4

1 Department of Physics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland

2 Condensed Matter Theory Group, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland

3 Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-2918, USA

4 Physics Department, University of California Santa Cruz, Santa Cruz, CA 95064, USA

* Corresponding authors emails: anelson@physik.uzh.ch
DOI10.24435/materialscloud:ng-f1 [version v1]

Publication date: Dec 13, 2021

How to cite this record

Aleksandra Nelson, Titus Neupert, Tomáš Bzdušek, Aris Alexandradinata, Multicellularity of delicate topological insulators, Materials Cloud Archive 2021.219 (2021), doi: 10.24435/materialscloud:ng-f1.


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.

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File name Size Description
36.6 KiB Code that generates data for figure 2 in the main text: bulk and surface Wannier functions for the delicate topological insulator; total polarization
9.3 KiB Code that generates data for figure 3 in the main text: polarization for the Hopf insulator
19.5 KiB Code that generates data for figure 4 in the main text: spectrum of Hopf-insulating and RTP-insulating slab
19.4 KiB Code that generates data for figure S2 in the supplementary material: stability of RTP invariant


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Journal reference (Published code generates data and figures for this paper)


topological insulators delicate topology multicellular Wannier functions returning Thouless pump Hopf insulator SNSF ERC H2020 MARVEL/DD6

Version history:

2021.219 (version v1) [This version] Dec 13, 2021 DOI10.24435/materialscloud:ng-f1