Four-band non-Abelian topological insulator and its experimental realization

Abstract

Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support non-trivial edge states that manifest the non-Abelian topological features. Furthermore, a system with even or odd number of bands will exhibit significant difference in non-Abelian topological classifications. Up to now, there is scant research investigating the even-band non-Abelian topological insulators. Here, we both theoretically explored and experimentally realized a four-band PT (inversion and time-reversal) symmetric system, where two new classes of topological charges as well as edge states are comprehensively studied. We illustrate their difference from four-dimensional rotation senses on the stereographically projected Clifford tori. We show the evolution of bulk topology by extending the 1D Hamiltonian onto a 2D plane and provide the accompanying edge state distributions following an analytical method. Our work presents an exhaustive study of four-band non-Abelian topological insulators and paves the way to other even band systems.

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References in corpus (31)

• Topological Insulators
• Topological insulators and superconductors
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Photonics
• Classification of topological insulators and superconductors in three spatial dimensions
• Photonic Floquet Topological Insulators
• Classification of topological quantum matter with symmetries
• Periodic table for topological insulators and superconductors
• Imaging topological edge states in silicon photonics
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• A single photonic cavity with two independent physical synthetic dimensions
• Non-Abelian band topology in noninteracting metals
• Non-Abelian reciprocal braiding of Weyl points and its manifestation in $\text{ZrTe}$
• Topological Euler class as a dynamical observable in optical lattices
• Experimental observation of non-Abelian topological charges and bulk-edge correspondence
• Observation of non-Abelian topological semimetals and their phase transitions
• Twisted bilayer graphene. II. Stable symmetry anomaly
• Non-Abelian Dirac node braiding and near-degeneracy of correlated phases at odd integer filling in magic angle twisted bilayer graphene
• Geometric approach to fragile topology beyond symmetry indicators
• Observation of non-Abelian nodal links in photonics
• 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
• Topological circuits of inductors and capacitors
• Observation of Three-dimensional Photonic Dirac points and Spin-polarized Surface Arcs
• Four-band non-Abelian topological insulator and its experimental realization
• From triple-point materials to multiband nodal links
• Universal higher-order bulk-boundary correspondence of triple nodal points
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Effective response theory for zero energy Majorana bound states in three spatial dimensions
• Rotations of the three-sphere and symmetry of the Clifford torus

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• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Non-Abelian Hopf-Euler insulators
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Wave packet dynamics and edge transport in anomalous Floquet topological phases
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Andreev reflection in Euler materials
• Synthetic non-Abelian topological charges in ultracold atomic gases
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Floquet non-Abelian topological charges and edge states
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Euler band topology in superfluids and superconductors
• Fermionic atoms in a spin-dependent optical lattice potential: topological insulators with broken time-reversal symmetry
• Hinge modes of three-dimensional Euler insulators
• Asymmetric real topology of conduction and valence bands
• Coupled-wire construction of non-Abelian higher-order topological phases
• Three-dimensional spinless Euler insulators with rotational symmetry