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.

13 pages, 6 figures

References in corpus (19)

• Topological Insulators with Inversion Symmetry
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• 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
• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• The space group classification of topological band insulators
• Direct observation of corner states in second-order topological photonic crystal slabs
• Topology of crystalline insulators and superconductors
• Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator
• Realization of an anomalous Floquet topological system with ultracold atoms
• An Aharonov-Bohm interferometer for determining Bloch band topology
• Fractional Bloch oscillations in photonic lattices
• Topological swing in Bloch oscillations
• Bloch oscillations of topological edge modes
• Controlling coherence via tuning of the population imbalance in a bipartite optical lattice

Cited by in corpus (20)

• 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
• Chiral Dynamics of Ultracold Atoms under a Tunable SU(2) Synthetic Gauge Field
• Non-Abelian tensor Berry connections in multi-band topological systems
• 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 Chern band in rhombohedral graphene multilayers
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Optical Absorption and Emission from Wannier-Stark Spectra of Moiré Superlattices
• Anomalous Bloch oscillation and electrical switching of edge magnetization in bilayer graphene nanoribbon
• Anomalous Topological Bloch Oscillations under Non-Abelian Gauge Fields
• Experimental Proposal on Non-Abelian Aharonov-Bohm Caging Effect with a Single Trapped Ion
• An exactly solvable model for anyons with non-Abelian flux