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Quasicrystalline analog of the Haldane model

B. D. K. Burgess* and N. R. Cooper

  • *Contact author: bb611@cam.ac.uk
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Phys. Rev. Research 8, 033105 – Published 27 July, 2026

DOI: https://doi.org/10.1103/2556-3lw6

Abstract

We present a model for a topological quasicrystalline system that is suitable for realization in cold atom experiments. We define the model in terms of complex momentum-space couplings that break time-reversal symmetry (TRS) and detail how it may be experimentally realized using two-photon Raman couplings. In the weak-potential limit, we study the model analytically by calculating the band structure over a “quasi-Brillouin zone” (QBZ). We find symmetry-protected Dirac cones, which are gapped by a TRS-breaking term, resulting in a Chern number C=1. This provides a direct analogy to the Haldane model, but now in a quasicrystalline setting. We also infer the number of states below the topological gap from the QBZ area. We verify our analysis with numerical calculations of periodic approximants to our system, constructing a phase diagram in parameter space that shows a topological region extending beyond the weak-potential regime. We also find examples of narrow Chern bands with the potential for hosting strongly correlated physics. Our work raises questions about the nature of localization and strongly correlated states in Chern bands in quasiperiodic systems.

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Phys. Rev. Research 8, 033105– Published 27 July, 2026
  • Received 23 January 2026
  • Accepted 10 June 2026
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