Non-Abelian Bloch oscillations in higher-order topological insulators

Abstract

Bloch oscillations (BOs) are a fundamental phenomenon by which a wave packet undergoes a periodic motion in a lattice when subjected to an external force. Observed in a wide range of synthetic lattice systems, BOs are intrinsically related to the geometric and topological properties of the underlying band structure. This has established BOs as a prominent tool for the detection of Berry phase effects, including those described by non-Abelian gauge fields. In this work, we unveil a unique topological effect that manifests in the BOs of higher-order topological insulators through the interplay of non-Abelian Berry curvature and quantized Wilson loops. It is characterized by an oscillating Hall drift that is synchronized with a topologically-protected inter-band beating and a multiplied Bloch period. We elucidate that the origin of this synchronization mechanism relies on the periodic quantum dynamics of Wannier centers. Our work paves the way to the experimental detection of non-Abelian topological properties in synthetic matter through the measurement of Berry phases and center-of-mass displacements.

arXiv comment13 pages, 6 figures

References in corpus (66)

• Topological Insulators
• Topological insulators and superconductors
• Berry Phase Effects on Electronic Properties
• Maximally-localized generalized Wannier functions for composite energy bands
• Anomalous Hall effect
• Topological Insulators with Inversion Symmetry
• Topological Photonics
• Topological Field Theory of Time-Reversal Invariant Insulators
• Maximally localized Wannier functions: Theory and applications
• Experimental realisation of the topological Haldane model
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Direct Measurement of the Zak phase in Topological Bloch Bands
• Topolectrical circuit realization of topological corner modes
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Topological Bands for Ultracold Atoms
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• The space group classification of topological band insulators
• Topological Thouless Pumping of Ultracold Fermions
• Direct observation of corner states in second-order topological photonic crystal slabs
• Photonic quadrupole topological phases
• Topology of crystalline insulators and superconductors
• Observation of second-order topological insulators in sonic crystals
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• Observation of half-integer thermal Hall conductance
• Quantized Faraday and Kerr rotation and axion electrodynamics of a 3D topological insulator
• Realization of an anomalous Floquet topological system with ultracold atoms
• Topological classification with additional symmetries from Clifford algebras
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Experimental observation of Aharonov-Bohm cages in photonic lattices
• Experimental Measurement of the Berry Curvature from Anomalous Transport
• Wannier Center Sheets in Topological Insulators
• Mapping the Berry Curvature from Semiclassical Dynamics in Optical Lattices
• Measuring topology by dynamics: Chern number from linking number
• Bloch state tomography using Wilson lines
• Fractional Bloch oscillations in photonic lattices
• Measuring quantized circular dichroism in ultracold topological matter
• Bloch oscillations in the absence of a lattice
• Quadrupole Topological Photonic Crystals
• Higher-order topological insulators in synthetic dimensions
• Detecting Topological Phases in Cold Atoms
• Berry-phase description of Topological Crystalline Insulators
• Semi-classical wave packet dynamics in non-uniform electric fields
• Effective Theory of Non-Adiabatic Quantum Evolution Based on the Quantum Geometric Tensor
• A two-leg Su-Schrieffer-Heeger chain with glide reflection symmetry
• Topological Bloch oscillations
• Measuring Z2 topological invariants in optical lattices using interferometry
• Realization of a fractional period adiabatic superlattice
• Topological swing in Bloch oscillations
• Imaging topology of Hofstadter ribbons
• Emergent periodic and quasiperiodic lattices on surfaces of synthetic Hall tori and synthetic Hall cylinders
• Bloch oscillations of topological edge modes
• Controlling coherence via tuning of the population imbalance in a bipartite optical lattice
• Nodal Brillouin Zone Boundary from Folding a Chern Insulator
• Chirality polarizations and spectral bulk-boundary correspondence
• Distinguishing trivial and topological quadrupolar insulators by Wannier-Stark ladders

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• Classical higher-order topological insulators
• Observation of Non-Abelian Thouless Pump
• Non-abelian Thouless pumping in a photonic lattice
• Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension
• Bose-Einstein Condensate on a Synthetic Topological Hall Cylinder
• Chiral Dynamics of Ultracold Atoms under a Tunable SU(2) Synthetic Gauge Field
• Non-Abelian tensor Berry connections in multi-band topological systems
• Wilson loop and Wilczek-Zee phase from a non-Abelian gauge field
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Universal semiclassical equations based on the quantum metric
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Chiral orbital order of interacting bosons without higher bands
• Topological Phases for Extended Objects: Semiclassical Phase-Space Approach with Tensorial Coordinates
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Non-Abelian Chern band in rhombohedral graphene multilayers
• Optical Absorption and Emission from Wannier-Stark Spectra of Moiré Superlattices
• Anomalous Topological Bloch Oscillations under Non-Abelian Gauge Fields
• Anomalous Bloch oscillation and electrical switching of edge magnetization in bilayer graphene nanoribbon
• An exactly solvable model for anyons with non-Abelian flux
• Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion