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Researchers identified quadrupole topological order in gyromagnetic photonic crystals, revealing quantized invariants and unique boundary states like fractional corner charges. This work extends topological concepts to realistic materials and Maxwell

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Area of Science:

  • Condensed Matter Physics
  • Topological Matter
  • Photonic Crystals

Background:

  • Quadrupole topological phases feature protected boundary states, acting as lower-dimensional topological insulators.
  • Extending these concepts to realistic materials necessitates quantized invariants for bulk quadrupole order.

Purpose of the Study:

  • To identify the analog of quadrupole order in Maxwell's equations for gyromagnetic photonic crystals.
  • To establish quantized invariants and explore boundary phenomena in these systems.

Main Methods:

  • Utilized a double-band-inversion process within Maxwell's equations.
  • Employed symmetry eigenvalue analysis, nested Wannier band calculations, and quadrupole operator expectation values.
  • Investigated boundary manifestations including edge polarizations and corner charges.

Main Results:

  • Identified quantized quadrupole moment in gyromagnetic photonic crystals under crystalline symmetry and broken time-reversal symmetry.
  • Confirmed quantization through three independent methods.
  • Revealed boundary states: quantized edge polarizations and fractional corner charges due to band filling anomalies.

Conclusions:

  • Demonstrated the existence and characterization of quadrupole topological phases in photonic systems.
  • Extended the understanding of topological invariants and boundary phenomena beyond electronic systems.
  • Opened avenues for realizing novel topological states in realistic metamaterials.