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Higher-order topological parity anomaly and half-integer quantum Hall effect in high-dimensional synthetic lattices

Xian-Hao Wei1,2,3, Xi-Wang Luo1,2,3,4,5,*, Guang-Can Guo1,2,3,5, and Zheng-Wei Zhou1,2,3,4,5,†

  • *Contact author: luoxw@ustc.edu.cn
  • †Contact author: zwzhou@ustc.edu.cn
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Phys. Rev. Research 8, 013293 – Published 17 March, 2026

DOI: https://doi.org/10.1103/vtqw-7yjf

Abstract

Recent advances in constructing synthetic dimension provide a powerful tool for exploring exotic topological states of matter in high dimensions. Here, we report that the parity anomaly and associated half-integer quantized Hall conductance, arising in 2j+1 (space-time) dimensions with a single or odd number of Dirac cones, can be realized by the boundary states of nth-order topological insulators in (2j+n)-dimensional synthetic lattices. We establish a general bulk-boundary correspondence by integrating the nested Wilson loop theory with the time-reversal polarization at highly symmetric momenta; a set of Z2 topological invariants are extracted, which determines the number and location of higher-order-boundary Dirac cones that are protected by time-reversal and reflection symmetries. We develop a general construction procedure for Hamiltonians supporting such higher-order topological parity anomaly. Moreover, we propose an experimental implementation scheme based on photonic synthetic dimensions and provide a method for probing the associated half-integer Hall conductance by the transmission spectra. Our work offers the realization and characterization of parity anomaly in general high-dimensional higher-order topological insulators and opens an avenue for exploring fundamental physics and possible photonic device applications enabled by manipulating Dirac cones.

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Phys. Rev. Research 8, 013293– Published 17 March, 2026
  • Received 24 March 2025
  • Accepted 23 February 2026
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