Band topology in classical waves: Wilson-loop approach to topological numbers and fragile topology

Abstract

The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical calculation of the topological invariants for several photonic/sonic crystals. We demonstrate that these topological photonic/sonic crystals are topological crystalline insulators with fragile topology, a feature which has been ignored in previous studies. We further discuss the bulk-edge correspondence in these systems with emphasis on symmetry broken on the edges.

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• Twisted quadrupole topological photonic crystals
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Topological Photonic Tamm-States and the Su-Schrieffer-Heeger Model
• Topological state transfer in Kresling origami
• Photonic corner skin modes
• Corner states and topological transitions in two-dimensional higher-order topological sonic crystals with inversion symmetry
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• Cubic 3D Chern photonic insulators with orientable large Chern vectors
• Local markers for crystalline topology
• Comparative study of Hermitian and non-Hermitian topological dielectric photonic crystals
• Driven quantum many-body systems and out-of-equilibrium topology
• Topological Graphene plasmons in a plasmonic realization of the Su-Schrieffer-Heeger Model
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
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• Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models
• Topological edge states in equidistant arrays of Lithium Niobate nano-waveguides
• Topological superconductivity in Fibonacci quasicrystals
• A General Method to Design Acoustic Higher-Order Topological Insulators
• Topological Corner States in Graphene by Bulk and Edge Engineering
• Versatile Braiding of Non-Hermitian Topological Edge States
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Dynamical Fragile Topology in Floquet Crystals
• Spontaneously-Induced Dirac Boundary State and Digitization in a Nonlinear Resonator Chain
• All-optical control of topological valley transport in graphene metasurfaces
• Multiple polaritonic edge states in a Su-Schrieffer-Heeger chain strongly coupled to a multimode cavity
• Small mode volume topological photonic states in one-dimensional lattices with dipole--quadrupole interactions
• Topological properties of a class of generalized Su-Schrieffer-Heeger networks: chains and meshes
• Realization of topological superlattices and the associated interface states in one-dimensional plasmonic crystals
• Probing fragile topology with a screw dislocation
• PT-symmetric Non-Hermitian Hopf Metal
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Topological photonic crystal fibre
• Topological gap solitons in equidistant lithium niobate waveguide arrays
• Tunable zero modes and quantum interferences in flat-band topological insulators
• Flat bands and topological phase transition in entangled Su-Schrieffer-Heeger chains
• Magnetic doping-induced second-order and first-order topological phase transition inthe photonic alloy
• Mirror-induced effects in cavity polaritonics: Influence on edge states
• Wilson Loop and Topological Properties in 3D Woodpile Photonic Crystal
• Topological phase transition and its stability against an applied magnetic field in a class of low dimensional decorated lattices
• Antichiral edge states and Bogoliubov Fermi surfaces in a two-dimensional proximity-induced superconductor
• Lithium Niobate Photonic Topological Insulator-based Multi-Wavelength Optical Demultiplexer with Piezoelectric Switch-Off
• Screened topological plasmons in graphene plasmonic crystals
• Triply degenerate nodal line and tunable contracted-drumhead surface state in a tight-binding model
• Group Structure of Wilson Loops in 2D Models with 2- and 4-Band Energy Spectra