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Title: 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.

Authors:
ORCiD logo; ORCiD logo; ORCiD logo
Publication Date:
Research Org.:
Princeton Univ., NJ (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1536842
DOE Contract Number:  
SC0016239
Resource Type:
Journal Article
Journal Name:
Science
Additional Journal Information:
Journal Volume: 357; Journal Issue: 6346; Journal ID: ISSN 0036-8075
Publisher:
AAAS
Country of Publication:
United States
Language:
English
Subject:
Science & Technology - Other Topics

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. doi:10.1126/science.aah6442.
Benalcazar, Wladimir A., Bernevig, B. Andrei, and Hughes, Taylor L. Thu . "Quantized electric multipole insulators". United States. doi:10.1126/science.aah6442.
@article{osti_1536842,
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},
issn = {0036-8075},
number = 6346,
volume = 357,
place = {United States},
year = {2017},
month = {7}
}

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