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Quantized electric multipole insulators.

Wladimir A Benalcazar1, B Andrei Bernevig2, Taylor L Hughes3

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|July 8, 2017
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Summary
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We reveal how higher electric multipole moments, like quadrupole and octupole, can be topologically quantized in crystals. This discovery introduces novel topological phases with exotic boundary states and fractional charges.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Materials Science

Background:

  • The Berry phase offers a modern framework for understanding electric polarization in crystalline solids.
  • Topological concepts are increasingly vital for classifying phases of matter beyond conventional approaches.

Purpose of the Study:

  • To extend the Berry phase formulation to higher electric multipole moments (quadrupole, octupole).
  • To identify conditions and minimal models for topological quantization of these multipole moments.
  • To explore the implications for topological phase classification and experimental realization.

Main Methods:

  • Utilizing the Berry phase formalism to analyze electric multipole moments.
  • Developing minimal model systems exhibiting topological quantization.
  • Introducing a novel characterization method using "nested" Wilson loops for topological invariants.
  • Investigating boundary phenomena, including gapped boundaries and corner states.

Main Results:

  • Demonstrated that quadrupole and octupole moments can be topologically quantized observables.
  • Identified gapped boundaries that act as lower-dimensional topological phases.
  • Discovered topologically protected corner states with fractional charge, a phenomenon of boundary fractionalization.
  • Introduced a new class of topological invariants derived from "nested" Wilson loops.

Conclusions:

  • The study expands the classification of topological phases of matter by incorporating higher electric multipole moments.
  • Proposed three experimentally testable implementations of the observed topological phenomena.
  • Opens new avenues for exploring topological matter and its unique electromagnetic properties.