Quantized electric multipole insulators
Abstract
The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.
- Publication Date:
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1437675
- Grant/Contract Number:
- award271391; SC0016239
- Resource Type:
- Published Article
- Journal Name:
- Science
- Additional Journal Information:
- Journal Name: Science Journal Volume: 357 Journal Issue: 6346; Journal ID: ISSN 0036-8075
- Publisher:
- American Association for the Advancement of Science (AAAS)
- Country of Publication:
- United States
- Language:
- English
Citation Formats
Benalcazar, Wladimir A., Bernevig, B. Andrei, and Hughes, Taylor L. Quantized electric multipole insulators. United States: N. p., 2017.
Web. doi:10.1126/science.aah6442.
Benalcazar, Wladimir A., Bernevig, B. Andrei, & Hughes, Taylor L. Quantized electric multipole insulators. United States. https://doi.org/10.1126/science.aah6442
Benalcazar, Wladimir A., Bernevig, B. Andrei, and Hughes, Taylor L. Thu .
"Quantized electric multipole insulators". United States. https://doi.org/10.1126/science.aah6442.
@article{osti_1437675,
title = {Quantized electric multipole insulators},
author = {Benalcazar, Wladimir A. and Bernevig, B. Andrei and Hughes, Taylor L.},
abstractNote = {The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electric multipole moments and determine the necessary conditions and minimal models for which the quadrupole and octupole moments are topologically quantized electromagnetic observables. Such systems exhibit gapped boundaries that are themselves lower-dimensional topological phases. Furthermore, they host topologically protected corner states carrying fractional charge, exhibiting fractionalization at the boundary of the boundary. To characterize these insulating phases of matter, we introduce a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked. We propose three realistic experimental implementations of this topological behavior that can be immediately tested. Our work opens a venue for the expansion of the classification of topological phases of matter.},
doi = {10.1126/science.aah6442},
journal = {Science},
number = 6346,
volume = 357,
place = {United States},
year = {Thu Jul 06 00:00:00 EDT 2017},
month = {Thu Jul 06 00:00:00 EDT 2017}
}
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