articleScienceJul 7, 2017GREEN OA

Quantized electric multipole insulators

WAWladimir A. BenalcazarBAB. Andrei BernevigTLTaylor L. Hughes

University of Illinois Urbana-Champaign · Princeton University

PubMed
Indexed inarxivcrossrefpubmed

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…

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1,909
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Authors

3
  • WA
    Wladimir A. BenalcazarCorresponding

    University of Illinois Urbana-Champaign

  • BA
    B. Andrei Bernevig

    Princeton University

  • TL
    Taylor L. Hughes

    University of Illinois Urbana-Champaign

Topics & keywords

Topics
Keywords
  • Multipole expansion
  • Fractionalization
  • Quadrupole
  • Polarization (electrochemistry)
  • Topological insulator
  • Topology (electrical circuits)
  • Polarization density
  • Boundary (topology)
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