Helical Dirac Current with Local Coupling to a Chiral Potential
Abstract
We show that a propagating electron wave in the lowest cylindrical channel carries a spin-resolved helical conserved current, and connect this current texture to its local chiral coupling. In a weakly relativistic positive-energy Dirac projection, the two sectors have the same azimuthally symmetric charge density and opposite circulation superposed on longitudinal flow, even though their nonrelativistic orbital harmonic is l=0. The current is radially distributed and extends into the evanescent tail. A scalar screw potential couples these modes through a derived vertex expressed by the \emph{chiral current overlap}, 𝒥χ. Both spatial textures determine the coupling: the environmental radial profile weights the electronic circulation, while the screw harmonic selects correlated changes of spin sector and longitudinal momentum. For a uniform static harmonic, elastic energy conservation makes the first-order spin-flip amplitude vanish within the same transverse mode. Environmental energy exchange is therefore required to activate these selected channels. The same current overlap supplies the spatial kernel for heliciton-assisted inelastic scattering in a companion study and for a subsequent transport treatment of chirality-induced spin selectivity (CISS).
Related
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BibTeX
@misc{gao2026helical,
title = {{Helical Dirac Current with Local Coupling to a Chiral Potential}},
author = {Ju Gao and Fang Shen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.17618},
eprint = {2606.17618},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.17618},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Helical Dirac Current with Local Coupling to a Chiral Potential
AU - Ju Gao
AU - Fang Shen
PY - 2026
DA - 2026/10/10
PB - arXiv
DO - 10.48550/arxiv.2606.17618
UR - https://arxiv.org/abs/2606.17618
AB - We show that a propagating electron wave in the lowest cylindrical channel carries a spin-resolved helical conserved current, and connect this current texture to its local chiral coupling. In a weakly relativistic positive-energy Dirac projection, the two sectors have the same azimuthally symmetric charge density and opposite circulation superposed on longitudinal flow, even though their nonrelativistic orbital harmonic is l=0. The current is radially distributed and extends into the evanescent tail. A scalar screw potential couples these modes through a derived vertex expressed by the \emph{chiral current overlap}, 𝒥_χ. Both spatial textures determine the coupling: the environmental radial profile weights the electronic circulation, while the screw harmonic selects correlated changes of spin sector and longitudinal momentum. For a uniform static harmonic, elastic energy conservation makes the first-order spin-flip amplitude vanish within the same transverse mode. Environmental energy exchange is therefore required to activate these selected channels. The same current overlap supplies the spatial kernel for heliciton-assisted inelastic scattering in a companion study and for a subsequent transport treatment of chirality-induced spin selectivity (CISS).
ER -