Demonstration of non-Abelian frame charge flow in photonic crystals

Abstract

In PT symmetric systems, the notion of non-Abelian frame charges enables multiband topological characterization of the degeneracy nodes through examining the eigenvector frame rotations. Interestingly, some features of these frame charges can be viewed as an analogue of electric charges confined in conducting wires, only that they flow in momentum space along nodal lines. However, these frame charges are not integers, and non-Abelian signatures emerge when braiding between adjacent band nodal lines occurs, which flips the direction of the flow. In photonic systems, we discover that the photonic Γ point serves as the source or sink of such frame charge flow due to a hidden braiding induced by the often-ignored electrostatic mode at zero-frequency. We use biaxial photonic crystals as examples and show how complex nodal line configurations can be explained as the topological consequences of the frame charge flow from the Γ point to the Brillouin zone boundaries. We further designed and fabricated meta-crystals to experimentally observe these line nodes as manifestation of the non-Abelian frame charge flow.

References in corpus (35)

• Topological Photonics
• Topological Photonics
• Experimental observation of Weyl points
• Topological nodal line semimetals with and without spin-orbital coupling
• Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite Cu${}_3$PdN
• Topological Node-Line Semimetal in Three Dimensional Graphene Networks
• Nodal-chain metals
• Nodal-link semimetals
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Non-Abelian band topology in noninteracting metals
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Nodal-knot semimetals
• Topological Euler class as a dynamical observable in optical lattices
• Hyperbolic Weyl point in reciprocal chiral metamaterial
• Experimental discovery of nodal chains
• Experimental observation of non-Abelian topological charges and bulk-edge correspondence
• Observation of non-Abelian topological semimetals and their phase transitions
• Observation of non-Abelian nodal links in photonics
• Weyl-link semimetals
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Non-abelian topology of nodal-line rings in $\mathcal{P}\mathcal{T}$-symmetric systems
• Observation of Non-Abelian Thouless Pump
• Topological acoustic triple point
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Kramers Nodal Line Metals
• Space-group theory of photonic bands
• Experimental observation of non-Abelian earring nodal links in phononic crystals
• From triple-point materials to multiband nodal links
• Non-Abelian charged nodal links in dielectric photonic crystal
• Topological continuum charges of acoustic phonons in 2D
• Location and topology of the fundamental gap in photonic crystals
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
• Photonic nodal lines with quadrupole Berry curvature distribution

Cited by in corpus (4)

• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Observation of Braid-Protected Unpaired Exceptional Points
• Coupled-wire construction of non-Abelian higher-order topological phases