Higher-order topological pumping and its observation in photonic lattices

Wladimir A. Benalcazar, Jiho Noh, Mohan Wang, Sheng Huang, Kevin P. Chen, and Mikael C. Rechtsman
Phys. Rev. B 105, 195129 – Published 20 May 2022

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.

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  • Received 19 June 2020
  • Revised 22 February 2022
  • Accepted 25 April 2022

DOI:https://doi.org/10.1103/PhysRevB.105.195129

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Wladimir A. Benalcazar1,*, Jiho Noh1,*, Mohan Wang2,*, Sheng Huang2,*, Kevin P. Chen2, and Mikael C. Rechtsman1

  • 1Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16801, USA
  • 2Department of Electrical and Computer Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

  • *These authors contributed equally.

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Vol. 105, Iss. 19 — 15 May 2022

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