Quantized electric multipole insulators
Top Cited Papers
- 7 July 2017
- journal article
- research article
- Published by American Association for the Advancement of Science (AAAS) in Science
- Vol. 357 (6346), 61-66
- https://doi.org/10.1126/science.aah6442
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.Keywords
Funding Information
- National Science Foundation (award271388, DMR 1351895-CAR,DMR-1420541,EAGER award)
- Office of Naval Research (award271389, N00014-14-1-0330)
- David and Lucile Packard Foundation (award271390)
- U.S. Department of Energy (award271391, DE-SC0016239)
- Army Research Office (award271392, MURI W911NF-12-1-0461)
- National Oceanic and Atmospheric Administration (award271393, AWD1004957)
- Alfred P. Sloan Foundation (award271394)
- Simons Foundation (award271395, Simons Investigator Award)
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