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Title: Twisted bulk-boundary correspondence of fragile topology

Abstract

A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
  1. Department of Physics, Princeton University Princeton, NJ 08544, USA.
  2. Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.
  3. Department of Physics, Princeton University Princeton, NJ 08544, USA., Physics Department, Freie Universitat Berlin Arnimallee 14, 14195 Berlin, Germany., Max Planck Institute of Microstructure Physics, 06120 Halle, Germany.
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1599697
Grant/Contract Number:  
[No. DE-SC0016239; No. DMR-142051; IT1301-19; No. 404513]
Resource Type:
Published Article
Journal Name:
Science
Additional Journal Information:
[Journal Name: Science Journal Volume: 367 Journal Issue: 6479]; Journal ID: ISSN 0036-8075
Publisher:
American Association for the Advancement of Science (AAAS)
Country of Publication:
United States
Language:
English

Citation Formats

Song, Zhi-Da, Elcoro, Luis, and Bernevig, B. Andrei. Twisted bulk-boundary correspondence of fragile topology. United States: N. p., 2020. Web. doi:10.1126/science.aaz7650.
Song, Zhi-Da, Elcoro, Luis, & Bernevig, B. Andrei. Twisted bulk-boundary correspondence of fragile topology. United States. doi:10.1126/science.aaz7650.
Song, Zhi-Da, Elcoro, Luis, and Bernevig, B. Andrei. Thu . "Twisted bulk-boundary correspondence of fragile topology". United States. doi:10.1126/science.aaz7650.
@article{osti_1599697,
title = {Twisted bulk-boundary correspondence of fragile topology},
author = {Song, Zhi-Da and Elcoro, Luis and Bernevig, B. Andrei},
abstractNote = {A topological insulator reveals its nontrivial bulk through the presence of gapless edge states: This is called the bulk-boundary correspondence. However, the recent discovery of “fragile” topological states with no gapless edges casts doubt on this concept. We propose a generalization of the bulk-boundary correspondence: a transformation under which the gap between the fragile phase and other bands must close. We derive specific twisted boundary conditions (TBCs) that can detect all the two-dimensional eigenvalue fragile phases. We develop the concept of real-space invariants, local good quantum numbers in real space, which fully characterize these phases and determine the number of gap closings under the TBCs. Realizations of the TBCs in metamaterials are proposed, thereby providing a route to their experimental verification.},
doi = {10.1126/science.aaz7650},
journal = {Science},
number = [6479],
volume = [367],
place = {United States},
year = {2020},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1126/science.aaz7650

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