Energy density as a probe of band representations in photonic crystals

Abstract

Topological Quantum Chemistry (TQC) has recently emerged as a instrumental tool to characterize the topological nature of both fermionic and bosonic band structures. TQC is based on the study of band representations and the localization of maximally localized Wannier functions. In this article, we study various two-dimensional photonic crystal structures analyzing their topological character through a combined study of TQC, their Wilson-loop spectra and the electromagnetic energy density. Our study demonstrates that the analysis of the spatial localization of the energy density complements the study of the topological properties in terms of the spectrum of the Wilson-loop operator and TQC.

References in corpus (39)

• Topological Insulators
• Maximally-localized generalized Wannier functions for composite energy bands
• Topological Photonics
• Topological Photonics
• Maximally localized Wannier functions: Theory and applications
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Quantized Electric Multipole Insulators
• Scheme to Achieve Silicon Topological Photonics
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Acoustics
• A topological quantum optics interface
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Fragile Topology and Wannier Obstructions
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Crystalline metamaterials for topological properties at subwavelength scales
• Unconventional quantum optics in topological waveguide QED
• A Short Introduction to Topological Quantum Computation
• Quantum Simulation with Interacting Photons
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Topology of Disconnected Elementary Band Representations
• Spinless Topological Insulators without Time-Reversal Symmetry
• A perspective on topological nanophotonics: current status and future challenges
• Band Representations and Topological Quantum Chemistry
• Tutorial: Computing topological invariants in two-dimensional photonic crystals
• Topological Properties of Electrons in Honeycomb Lattice with Kekulé Hopping Textures
• Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light
• Symmetry representation approach to topological invariants in $C_{2z}T$-symmetric systems
• Topological quantum optics using atom-like emitter arrays coupled to photonic crystals
• On the robustness of topological corner modes in photonic crystals
• Topological photonics: from crystals to particles
• Higher-order topology in plasmonic kagome lattices
• Corner modes of the breathing kagome lattice: origin and robustness
• Exciting Pseudospin Dependent Edge States in Plasmonic Metasurfaces
• GTPack: A Mathematica group theory package for application in solid-state physics and photonics
• Topology invisible to eigenvalues in obstructed atomic insulators
• Criteria for realizing room temperature electrical transport applications of topological materials
• Rapid Exploration of Topological Band Structures using Deep Learning
• Engineering Topological Phases Guided by Statistical and Machine Learning Methods

Cited by in corpus (4)

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• Topological Lasing from Thouless Pumping in Bilayer Photonic Crystal
• Wannier center spectroscopy to identify boundary-obstructed topological insulators