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  • Open Access

Quasiperiodicity Protects Quantized Transport in Disordered Systems Without Gaps

Emmanuel Gottlob1, Dan S. Borgnia2,*, Robert-Jan Slager3, and Ulrich Schneider1

  • *Contact author: dborgnia@berkeley.edu
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PRX Quantum 6, 020359 – Published 26 June, 2025

DOI: https://doi.org/10.1103/zvng-w46m

Abstract

The robustness of topological properties, such as quantized currents, generally depends on the existence of gaps surrounding the relevant energy levels or on symmetry-forbidden transitions. Here, we observe quantized currents that survive the addition of bounded local disorder beyond the closing of the relevant instantaneous energy gaps in a driven Aubry-André-Harper chain, a prototypical model of quasiperiodic systems. We explain the robustness using a local picture in configuration space based on Landau-Zener transitions, which rests on the Anderson localization of the eigenstates. Moreover, we propose a protocol, directly realizable in, for instance, cold atoms or photonic experiments, that leverages this stability to prepare topological many-body states with high Chern numbers and opens new experimental avenues for the study of both the integer and fractional quantum Hall effects.

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Popular Summary

We typically picture electrical current as countless electrons leaving a source, ricocheting off impurities, and finally draining into a sink; on laboratory length and time scales, the electronic random motion averages into an almost smooth flow. A topological charge pump behaves differently: each slow cycle of an external field moves the same exact number of particles across the system; the number is perfectly stable against a wide range of perturbations. Conventional wisdom attributes such precision to an energy gap separating occupied quantum states from empty states or to a mobility gap only protecting the occupation of delocalized states. Our work, however, shows that such gaps are not essential.

We focus on the one-dimensional Aubry-André-Harper lattice, whose incommensurate (quasiperiodic) modulation localizes single-particle states and sculpts the spectrum into a rigid, self-similar Hofstadter hierarchy. For this system, we find that quantization endures even after strong on-site disorder closes the mobility gap. Three ingredients enforce this robustness: (i) Anderson localization confines particles locally, (ii) the fractal set of minigaps constrains level crossings, and (iii) the drive rate can be chosen slow enough to suppress the few remaining long-range hops. Quantization is therefore protected by locality and quasiperiodicity rather than energetic isolation.

This dynamically protected channel can shuttle states of large Chern numbers without fine-tuning and relies only on on-site potentials and lattice phase modulation, ingredients already available in ultracold-atom lattices, photonic waveguides, and superconducting-qubit arrays, opening a new route to robust state preparation and noise-resilient transport for quantum information architectures.

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PRX Quantum 6, 020359– Published 26 June, 2025
  • Received 6 December 2024
  • Revised 11 May 2025
  • Accepted 28 May 2025
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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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