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Quantized electric multipole insulators

Author(s): Benalcazar, Wladimir A; Bernevig, Bogdan A.; Hughes, Taylor L

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Abstract: The Berry phase provides a modern formulation of electric polarization in crystals. We extend this concept to higher electricmultipole 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: 7-Jul-2017
Electronic Publication Date: 7-Jul-2017
Citation: Benalcazar, Wladimir A, Bernevig, B Andrei, Hughes, Taylor L. (2017). Quantized electric multipole insulators. SCIENCE, 357 (61 - 66. doi:10.1126/science.aah6442
DOI: doi:10.1126/science.aah6442
ISSN: 0036-8075
EISSN: 1095-9203
Pages: 61 - 66
Type of Material: Journal Article
Journal/Proceeding Title: SCIENCE
Version: Author's manuscript

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