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Localization and topological signatures under periodic twisting

James Walkling1,2,*, Antonio Štrkalj3,2,†,‡, and F. Nur Ünal4,2,†,§

  • *Contact author: jamwalk@pks.mpg.de
  • †These authors contributed equally to this work.
  • ‡Contact author: astrkalj@phy.hr
  • §Contact author: f.unal@bham.ac.uk
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Phys. Rev. Research 8, 023356 – Published 29 June, 2026

DOI: https://doi.org/10.1103/wt1y-69rf

Abstract

We theoretically explore a dynamical generalization of the Aubry-André model in two dimensions formed by superimposing two square-lattice potentials. Motivated by the rich physics emerging at different twist angles between the two lattices at equilibrium, we introduce periodic twisting by continuously rotating one of the lattices with respect to the other in the plane. We demonstrate that the distinct time-dependent twisting in this system gives rise to an intricate form of periodic multifrequency driving that changes with the distance from the rotation axis. We find that the incommensurate nature of the potential no longer plays the pivotal role as it does in the static case. Rather, the tunneling can be understood in terms of a local, spatially varying dynamical localization effect, which we show to yield ring-shaped states localized within the bulk that have interesting transport signatures. Quantifying the eigenstates with the Bott index and local Chern marker, we find that there is a zoo of states with nontrivial topological signatures, the most ubiquitous of which result in relatively uniform ring-shaped regions of the Chern marker. We investigate the origin of these effects from various angles and identify that hybridization between different delocalized ring states plays a vital role. Finally, we discuss possible experimental realizations in quantum simulation settings. Our results open an avenue of investigation with periodic twisting inducing a spatially varying multifrequency drive.

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Phys. Rev. Research 8, 023356– Published 29 June, 2026
  • Received 3 October 2025
  • Accepted 29 May 2026
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