Twisted bulk-boundary correspondence of fragile topology
[1];
[2];
[3]
- Department of Physics, Princeton University Princeton, NJ 08544, USA.
- Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Apartado 644, 48080 Bilbao, Spain.
- 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.
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.
- Sponsoring Organization:
- USDOE
- Grant/Contract Number:
- No. DE-SC0016239; No. DMR-142051; IT1301-19; No. 404513
- OSTI ID:
- 1599697
- Journal Information:
- Science, Journal Name: Science Vol. 367 Journal Issue: 6479; ISSN 0036-8075
- Publisher:
- American Association for the Advancement of Science (AAAS)Copyright Statement
- Country of Publication:
- United States
- Language:
- English
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