[Paper Review] Higher-order topological pumping

Wladimir A. Benalcazar, Jiho Noh+4 more|arXiv (Cornell University)|Jun 23, 2020

Topological Materials and Phenomena4 citations

TL;DR

This paper introduces higher-order topological pumping in two-dimensional photonic systems, demonstrating that adiabatic cycles with zero net particle transport can still exhibit nontrivial topology due to higher-order invariants. Experimentally verified using modulated photonic waveguide arrays, the mechanism enables corner-to-corner transport, analogous to chiral hinge states in 3D second-order topological insulators, extending Thouless pumping to higher-order topology.

ABSTRACT

The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Thouless D. J., 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 `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 this transport by using an array of photonic waveguides modulated in their separations and refractive indices. By mapping the dynamical phenomenon demonstrated here from two spatial and one temporal to three spatial dimensions, this transport is equivalent to the observation of the chiral nature of the gapless hinge states in a three-dimensional second-order topological insulator.

Motivation & Objective

• To extend Thouless pumping to higher-order topological invariants beyond conventional particle transport.
• To demonstrate that systems with vanishing dipole moments can still host nontrivial topological dynamics.
• To establish a dynamical realization of higher-order topology in periodically driven 2D systems.
• To experimentally verify corner-to-corner transport as a signature of higher-order topology in photonic platforms.
• To map dynamical pumping in 2D+1D to a 3D topological phase, linking to chiral hinge states in 3D second-order topological insulators.

Proposed method

• Use of adiabatic pumping cycles in two-dimensional photonic waveguide arrays with spatial and refractive index modulation.
• Engineering of systems with zero net dipole moment to isolate higher-order topological effects.
• Employment of time-periodic modulation to realize effective dynamical topological invariants.
• Mapping the 2D spatial + 1D temporal system to a 3D spatial topological phase to reveal chiral hinge modes.
• Experimental observation of unidirectional corner-to-corner transport as a signature of higher-order topology.
• Diagnosis of topological invariants via transport quantization and edge state localization.

Experimental results

Research questions

• RQ1 Can adiabatic pumping in 2D systems with zero dipole moment still exhibit nontrivial topology?
• RQ2 What topological invariant governs transport in such systems, and how does it differ from conventional Thouless pumping?
• RQ3 Can corner-to-corner transport be experimentally realized in photonic metamaterials under these conditions?
• RQ4 How does the dynamical system map to a 3D topological insulator with chiral hinge states?
• RQ5 What is the role of higher-order topology in enabling transport without net particle flow?

Key findings

• Adiabatic cycles in 2D crystals with zero dipole moment can still host nontrivial higher-order topology, despite vanishing net particle transport.
• The system exhibits quantized corner-to-corner transport in photonic waveguide arrays, experimentally confirmed via spatial beam profiling.
• The transport is topologically protected and robust against disorder, as demonstrated in the experimental setup.
• The dynamical system maps to a 3D second-order topological insulator, with chiral hinge modes emerging in the effective 3D space.
• The higher-order topological invariant governs the transport, distinct from the Chern number in conventional Thouless pumping.
• The experimental realization confirms the theoretical prediction of higher-order topological pumping in photonic platforms.