Parity-Anomalous Hall Response of Chiral Lifshitz Fermions
Abstract
The parity anomaly of a single massless Dirac fermion is manifested as a half-quantized Hall response once the required parity-breaking regularization is supplied. We study the corresponding response for two-dimensional chiral Lifshitz fermions. For a node with low-energy coupling (qx +iqy)^N, the Fermi-loop winding number W = N gives an anomalous Hall response σxy^anom = (W/2)e^2/h. We examine this mechanism in chiral multilayer Haldane models tuned to a valley-selective critical line, where a single gapless chiral Lifshitz fermion remains at the K valley. For the AB, ABC, and ABCA stacks, the projected pseudospin textures give W = 2, 3, 4, while Kubo calculations yield σxy = (1, 3/2, 2)e^2/h; integrated equilibrium boundary currents reproduce the same W/2 sequence. Six-terminal simulations with dephasing further show that the Hall conductivity is quantized at W/2 while the longitudinal conductivity remains finite. These results identify gapless chiral Lifshitz fermions as a higher-order, winding-controlled generalization of the parity-anomalous Hall response, distinct from a quantum anomalous Hall insulating state even when W/2 is an integer.
Versions
Related
- Single Dirac Fermions on a Lattice: A Unified View of Chiral and Parity Anomalies in Condensed Matter
- Parity anomaly governs the thermal Hall response of chiral superconductivity in rhombohedral graphene above and below Tc
- Higher derivative Hořava-Lifshitz fermions: from superconductivity to atomic spectroscopy
- Fermi surface and field-induced Lifshitz transition in the antiferromagnet NbMnP exhibiting an anomalous Hall effect
- A gauge-invariant measure for lattice chiral fermions
BibTeX
@misc{han2026parityanomalous,
title = {{Parity-Anomalous Hall Response of Chiral Lifshitz Fermions}},
author = {Yanmiao Han and Rundong Zhao and Yu-Hao Wan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13017},
eprint = {2610.13017},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13017},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Parity-Anomalous Hall Response of Chiral Lifshitz Fermions
AU - Yanmiao Han
AU - Rundong Zhao
AU - Yu-Hao Wan
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13017
UR - https://arxiv.org/abs/2610.13017
AB - The parity anomaly of a single massless Dirac fermion is manifested as a half-quantized Hall response once the required parity-breaking regularization is supplied. We study the corresponding response for two-dimensional chiral Lifshitz fermions. For a node with low-energy coupling (qx +iqy)^N, the Fermi-loop winding number W = N gives an anomalous Hall response σxy^anom = (W/2)e^2/h. We examine this mechanism in chiral multilayer Haldane models tuned to a valley-selective critical line, where a single gapless chiral Lifshitz fermion remains at the K valley. For the AB, ABC, and ABCA stacks, the projected pseudospin textures give W = 2, 3, 4, while Kubo calculations yield σxy = (1, 3/2, 2)e^2/h; integrated equilibrium boundary currents reproduce the same W/2 sequence. Six-terminal simulations with dephasing further show that the Hall conductivity is quantized at W/2 while the longitudinal conductivity remains finite. These results identify gapless chiral Lifshitz fermions as a higher-order, winding-controlled generalization of the parity-anomalous Hall response, distinct from a quantum anomalous Hall insulating state even when W/2 is an integer.
ER -