Local Markers for Crystalline Topology.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Photonics

Background:

• Topological crystalline phases in photonic crystals enable edge- and corner-localized states for enhanced light-matter interactions.
• Current band-theoretic methods fail to predict the existence, localization, or spectral isolation of these boundary states.
• Topological states at material interfaces are not guaranteed to be within the band gap, limiting practical applications.

Purpose of the Study:

• To derive a class of local markers for identifying material topology based on crystalline symmetries.
• To develop a measure of topological protection for these localized states.
• To establish a predictive framework for designing topological crystalline heterostructures.

Main Methods:

• Derivation of local markers based on crystalline symmetries to identify material topology.
• Development of a real-space-based approach for assessing topological protection.
• Application of the framework to predict and design topological crystalline heterostructures.

Main Results:

• A novel class of local markers successfully identifies material topology linked to crystalline symmetries.
• The real-space approach inherently reveals the existence and robustness of topological boundary-localized states.
• The framework provides a predictive tool for optimizing device geometries and heterostructures.

Conclusions:

• The developed local marker framework offers a predictive approach for designing topological crystalline heterostructures.
• This method enhances the utility of topological states in photonic devices by ensuring their spectral isolation within the band gap.
• The framework is anticipated to guide the derivation of local markers for other symmetry-reliant topological classes.