Collective Hall quantization in 3D Chern vector systems
Abstract
Understanding the three-dimensional (3D) quantum Hall effect, characterized by a Chern vector rather than a single Chern number, has been a central pursuit in topological physics. While quantized Hall transport is established for the special case with one nonzero Chern component, recent realizations of more general Chern-vector states raise a fundamental question: how does such topology protect quantized transport? Here, we predict a distinct 3D quantized Hall effect protected by C=(0,m,n). For samples with dimensions Ly and Lz, global topology enforces collective quantization of mLy+nLz, despite the fragility of individual edge modes to disorder. This reveals a novel transport regime in which robust quantization emerges as a holistic property of a unified chiral network,rather than of its constituent modes. Crucially, this collective response manifests as a quantized Hall conductance Gxy=±(mLy+nLz)e2/h, with a distinctive dependence on both Chern-vector components and sample dimensions. We propose candidate materials to facilitate experimental observation.
Related
- The Chern-Simons Function and the Quantum Hall Effect
- Attraction from repulsion in an interacting Chern band: chiral superconductivity, generalized Hall crystals, and competing fractional Chern insulators
- Spontaneous Chirality and Collective Chern Bands in a Dipole-Conserving Bose System
- Guiding center quantization of a quantum Hall analog of Hawking radiation
- Haldane-Holstein model at fractional filling: Route to bosonic fractional Chern insulator and quantum anomalous Hall crystal
BibTeX
@misc{zhang2026collective,
title = {{Collective Hall quantization in 3D Chern vector systems}},
author = {Zhi-Qiang Zhang and Shuguang Cheng and Hongfang Liu and Hailong Li and Hua Jiang and X. C. Xie},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27802},
eprint = {2610.27802},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27802},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collective Hall quantization in 3D Chern vector systems
AU - Zhi-Qiang Zhang
AU - Shuguang Cheng
AU - Hongfang Liu
AU - Hailong Li
AU - Hua Jiang
AU - X. C. Xie
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27802
UR - https://arxiv.org/abs/2610.27802
AB - Understanding the three-dimensional (3D) quantum Hall effect, characterized by a Chern vector rather than a single Chern number, has been a central pursuit in topological physics. While quantized Hall transport is established for the special case with one nonzero Chern component, recent realizations of more general Chern-vector states raise a fundamental question: how does such topology protect quantized transport? Here, we predict a distinct 3D quantized Hall effect protected by C=(0,m,n). For samples with dimensions L_y and L_z, global topology enforces collective quantization of mL_y+nL_z, despite the fragility of individual edge modes to disorder. This reveals a novel transport regime in which robust quantization emerges as a holistic property of a unified chiral network,rather than of its constituent modes. Crucially, this collective response manifests as a quantized Hall conductance G_xy=±(mL_y+nL_z)e^2/h, with a distinctive dependence on both Chern-vector components and sample dimensions. We propose candidate materials to facilitate experimental observation.
ER -