Higher-order topological pumping and its observation in photonic lattices

Abstract

The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in two-dimensional electron gases, with the topology of dynamical periodic systems in one dimension. Here, we demonstrate its counterpart for higher-order topology. Specifically, we show that adiabatic cycles in two-dimensional crystals with vanishing dipole moments (and therefore zero overall particle transport) can nevertheless be topologically nontrivial. These cycles are associated with higher-order topology and can be diagnosed by their ability to produce corner-to-corner transport in certain metamaterial platforms. We experimentally verify the corner to corner transport associated with this topological pump by using an array of photonic waveguides adiabatically modulated in their separations and refractive indices. By mapping the dynamical phenomenon demonstrated here from two spatial and one temporal dimensions to three spatial dimensions, our observations are equivalent to the observation of chiral hinge states in a three-dimensional second-order topological insulator.

arXiv comment12 pages, 8 figures

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• Thouless pumping and topology
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• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Observation of higher-order topological states on a quantum computer
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Quantized Topological Anderson-Thouless Pump
• Interacting Topological Quantum Chemistry in 2D: Many-body Real Space Invariants
• Quantized charge-pumping in higher-order topological insulators
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• High-order topological pumping on a superconducting quantum processor
• A semiclassical treatment of spinor topological effects in driven, inhomogeneous insulators under external electromagnetic fields
• Bulk-boundary correspondence in topological systems with the momentum dependent energy shift
• Floquet-Anderson localization in the Thouless pump and how to avoid it