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Emergent topological properties in spatially modulated sub-wavelength-barrier lattices

Giedrius Žlabys1,*, Wen-Bin He1, Domantas Burba2, Sarika Sasidharan Nair1, Thomas Busch1,†, and Tomoki Ozawa3

  • *Contact author: giedrius.zlabys@oist.jp
  • †Contact author: thomas.busch@oist.jp
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Phys. Rev. A 113, 043301 – Published 1 April, 2026

DOI: https://doi.org/10.1103/gf47-yh4z

Abstract

We investigate topological phenomena in a spatially modulated Dirac-δ lattice, where the scattering potential varies periodically in space. Changing the potential modulation frequency leads to Hofstadter's butterfly-like energy spectrum and enables the emergence of topological transport regimes characterized by nontrivial Chern numbers. We show how the considered modulated system is connected to the Hofstadter model via the Harper equation. By adiabatically varying spatial modulation parameters, we demonstrate controllable quantum transport and verify the topological nature of these effects through Wannier center displacement and bulk invariant calculations. We also propose an experimentally feasible realization of such a system using optically controlled three-level atoms. Our findings showcase spatially engineered Kronig–Penney-type systems as versatile platforms for investigating and exploiting different topological quantum transport regimes.

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Phys. Rev. A 113, 043301– Published 1 April, 2026
  • Received 22 December 2025
  • Accepted 2 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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