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.

Main text and supplementary information

References in corpus (9)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Euler class as a dynamical observable in optical lattices
• Observation of non-Abelian topological semimetals and their phase transitions
• Geometric approach to fragile topology beyond symmetry indicators
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Four-band non-Abelian topological insulator and its experimental realization
• 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

Cited by in corpus (20)

• Four-band non-Abelian topological insulator and its experimental realization
• Minimal non-abelian nodal braiding in ideal metamaterials
• Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension
• 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