Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase

Abstract

Topological phases of matter span a wide area of research shaping fundamental pursuits and offering promise for future applications. While a significant fraction of topological materials has been characterized using symmetry requirements of wave functions, the past two years have witnessed the rise of novel multi-gap dependent topological states, the properties of which go beyond these approaches and are yet to be fully explored. Thriving upon these insights, we report on uncharted anomalous phases and properties that can only arise in out-of-equilibrium Floquet settings. In particular, we identify Floquet-induced non-Abelian braiding mechanisms, which in turn lead to a phase characterized by an anomalous Euler class, the prime example of a multi-gap topological invariant. Most strikingly, we also retrieve the first example of an `anomalous Dirac string phase'. This gapped out-of-equilibrium phase features an unconventional Dirac string configuration that physically manifests itself via anomalous edge states on the boundary. Our results therefore not only provide a stepping stone for the exploration of intrinsically dynamical and experimentally viable multi-gap topological phases, but also demonstrate a powerful way to observe these non-Abelian processes notably in quantum simulators.

4+7 pages, 3+5 figures

References in corpus (22)

• Topological characterization of periodically-driven quantum systems
• The space group classification of topological band insulators
• Dynamical control of matter-wave tunneling in periodic potentials
• 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
• Geometric approach to fragile topology beyond symmetry indicators
• Topological correspondence between magnetic space group representations
• Phonons as a platform for non-Abelian braiding and its manifestation in layered silicates
• Bicircular light tuning of magnetic symmetry and topology in Dirac semimetal Cd${}_3$As${}_2$
• Topological acoustic triple point
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Quadratic band touching points and flat bands in two-dimensional topological Floquet systems
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Manipulation and braiding of Weyl nodes using symmetry-constrained phase transitions
• Topological properties of Floquet winding bands in a photonic lattice
• Topological continuum charges of acoustic phonons in 2D
• Direct Geometric Probe of Singularities in Band Structure
• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Interferometry of non-Abelian band singularities and Euler class topology
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Wave packet dynamics and edge transport in anomalous Floquet topological phases

Cited by in corpus (29)

• Quantized Integrated Shift Effect in Multigap Topological Phases
• Optical manifestations and bounds of topological Euler class
• Non-Abelian Hopf-Euler insulators
• Quantum Valley Hall effect without Berry curvature
• Interferometry of non-Abelian band singularities and Euler class topology
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Anomalous topological edge modes in a periodically-driven trimer lattice
• Anomalous geometric transport signatures of topological Euler class
• Synthetic non-Abelian topological charges in ultracold atomic gases
• Exact projected entangled pair ground states with topological Euler invariant
• Non-Bloch Theory for Spatiotemporal Photonic Crystals Assisted by Continuum Effective Medium
• Second Euler number in four dimensional synthetic matter
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Floquet non-Abelian topological charges and edge states
• Individually tunable tunnelling coefficients in optical lattices using local periodic driving
• Polarization textures in crystal supercells with topological bands
• Dynamical characterization of $Z_2$ Floquet topological phases via quantum quenches
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Emergent topological phases and coexistence of gapless and spectral-localized Floquet quantum spin Hall states via electron-phonon interaction
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Anomalous multi-gap topological phases in periodically driven quantum rotors
• Non-Abelian interference of topological edge states
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Topology and edge modes surviving criticality in non-Hermitian Floquet systems
• Coupled-wire construction of non-Abelian higher-order topological phases
• Orbital magnetization reveals multiband topology
• Localization and topological signatures under periodic twisting
• Hinge modes of three-dimensional Euler insulators