Engineering Fragile Topology in Photonic Crystals: Topological Quantum Chemistry of Light

Abstract

In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport of light and quantum information at macroscopic scales. In this work, we apply for the first time the recently developed theory of "Topological quantum chemistry" to the study of band structures in photonic crystals. This method allows us to design and diagnose topological photonic band structures using only group theory and linear algebra. As an example, we focus on a family of crystals formed by elliptical rods in a triangular lattice. We show that the symmetry of Bloch states in the Brillouin zone can determine the position of the localized photonic wave packets describing groups of bands. By modifying the crystal structure and inverting bands, we show how the centers of these wave packets can be moved between different positions in the unit cell. Finally, we show that for shapes of dielectric rods, there exist isolated topological bands which do not admit a well-localized description, representing the first physical instance of "fragile" topology in a truly noninteracting system. Our work demonstrates how photonic crystals are the natural platform for the future experimental investigation of fragile topological bands.

arXiv commentv1. 4 pages + references main text, 5+epsilon page supplementary material v2. Published version, 4pgs + references. Supplemental material available at https://doi.org/10.1103/PhysRevResearch.1.032005

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• Fractional corner charges in spin-orbit coupled crystals
• On the robustness of topological corner modes in photonic crystals
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Topological photonics: fundamental concepts, recent developments, and future directions
• Strong interlayer coupling and stable topological flat bands in twisted bilayer photonic Moire superlattices
• Higher-order topology in plasmonic kagome lattices
• Fragile topology in line-graph lattices with two, three, or four gapped flat bands
• Berry bands and pseudo-spin of topological photonic phases
• Manipulating Topological Valley Modes in Plasmonic Metasurfaces
• Local markers for crystalline topology
• Tunable Fragile Topology in Floquet Systems
• Hybrid topological guiding mechanisms for photonic crystal fibers
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Location and topology of the fundamental gap in photonic crystals
• Rapid Exploration of Topological Band Structures using Deep Learning
• Fragile phonon topology on the honeycomb lattice with time-reversal symmetry
• Absence of topological protection of the interface states in ${\mathbb{Z}}_2$ photonic crystals
• Lecture Notes on Berry Phases and Topology
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Fractional corner charges in a 2D super-lattice Bose-Hubbard model
• From Atomic Semimetal to Topological Nontrivial Insulator
• Dynamics of self-dual kagome metamaterials and the emergence of fragile topology
• Near- and Far-Field Excitation of Topological Plasmonic Metasurfaces
• Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models
• Dynamical Fragile Topology in Floquet Crystals
• Energy density as a probe of band representations in photonic crystals
• Band alignment effect in the topological photonic alloy
• Wannier center spectroscopy to identify boundary-obstructed topological insulators
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Fractional corner charges in threefold-symmetric two-dimensional materials with fragile topology
• Fragile topological phase on the triangular kagome lattice and its bulk-boundary correspondence
• Omnidirectional domain wall modes protected by fragile topological states
• Simple realization of a fragile topological lattice with quasi flat-bands in a microcavity array
• IrRep: symmetry eigenvalues and irreducible representations of ab initio band structures
• Transversality-Enforced Tight-Binding Models for 3D Photonic Crystals aided by Topological Quantum Chemistry
• PT-symmetric Non-Hermitian Hopf Metal
• Topological property of graphene with triangular array of nanoholes