Helical Anomaly from Concurrent ℤ and ℤ2 Topology in an Acoustic Semimetal
Abstract
Topological classification constitutes a cornerstone of modern condensed-matter physics. Historically, topological systems have been predominantly characterized by invariants confined to a single topological class, such as topological insulators with a ℤ2 invariant and Weyl semimetals with an integer (ℤ) topological charge. While such classification frameworks in principle permit gapless phases in which bulk and boundary degeneracies are protected by distinct invariants, this regime has received limited focused attention, as coordinating the requisite symmetries within a single band structure is highly nontrivial. Here, we realize such concurrent ℤ and ℤ2 topology in a two-dimensional acoustic semimetal, revealing pseudospin-selective topological bulk modes arising from the interplay between these distinct invariants, termed helical anomaly bulk states (HABSs). Our lattice design exploits layer, sublattice, and gauge-staggered degrees of freedom, enabling modular control of effective time-reversal, chiral, and particle-hole symmetries. The resulting system exhibits bulk degeneracies protected by an integer ℤ invariant and Kramers-like boundary degeneracies protected by a ℤ2 invariant, forming twisted boundary arcs. Crucially, finite-size systems manifest helical or anti-helical edge states coexisting with HABSs, a distinctive signature absent in single-invariant topologies. Our results establish HABSs as a characteristic signature of concurrent topology and demonstrate a new regime where bulk and boundary invariants jointly govern topological transport beyond conventional single-class frameworks.
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BibTeX
@misc{li2026helical,
title = {{Helical Anomaly from Concurrent $\mathbbZ$ and $\mathbbZ_2$ Topology in an Acoustic Semimetal}},
author = {Hou-Yin Li and Hua-Shan Lai and Jian-Lan Xie and Xiao-Chen Sun and Yan-Feng Chen and Cheng He},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.28125},
eprint = {2609.28125},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.28125},
}
RIS
TY - UNPB
TI - Helical Anomaly from Concurrent ℤ and ℤ_2 Topology in an Acoustic Semimetal
AU - Hou-Yin Li
AU - Hua-Shan Lai
AU - Jian-Lan Xie
AU - Xiao-Chen Sun
AU - Yan-Feng Chen
AU - Cheng He
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.28125
UR - https://arxiv.org/abs/2609.28125
AB - Topological classification constitutes a cornerstone of modern condensed-matter physics. Historically, topological systems have been predominantly characterized by invariants confined to a single topological class, such as topological insulators with a ℤ_2 invariant and Weyl semimetals with an integer (ℤ) topological charge. While such classification frameworks in principle permit gapless phases in which bulk and boundary degeneracies are protected by distinct invariants, this regime has received limited focused attention, as coordinating the requisite symmetries within a single band structure is highly nontrivial. Here, we realize such concurrent ℤ and ℤ_2 topology in a two-dimensional acoustic semimetal, revealing pseudospin-selective topological bulk modes arising from the interplay between these distinct invariants, termed helical anomaly bulk states (HABSs). Our lattice design exploits layer, sublattice, and gauge-staggered degrees of freedom, enabling modular control of effective time-reversal, chiral, and particle-hole symmetries. The resulting system exhibits bulk degeneracies protected by an integer ℤ invariant and Kramers-like boundary degeneracies protected by a ℤ_2 invariant, forming twisted boundary arcs. Crucially, finite-size systems manifest helical or anti-helical edge states coexisting with HABSs, a distinctive signature absent in single-invariant topologies. Our results establish HABSs as a characteristic signature of concurrent topology and demonstrate a new regime where bulk and boundary invariants jointly govern topological transport beyond conventional single-class frameworks.
ER -