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Helical Current of Propagating Dirac Electrons and Geometric Coupling to Chiral Environments

Ju Gao, Fang Shen

Abstract

We show that a propagating Dirac electron with intrinsic spin generically carries a real--space helical conserved current, even in the absence of orbital angular momentum. Using exact Dirac eigenstates in cylindrical confinement, we demonstrate that this helical structure possesses definite handedness, persists into evanescent regions, and is characterized by a geometric helix pitch independent of the longitudinal de~Broglie wavelength. This intrinsic helical geometry enables a local geometric coupling between a propagating electron and a chiral environment, yielding chirality--dependent spin selectivity through current geometry rather than through a spin--orbit coupling term.

Helical Current of Propagating Dirac Electrons and Geometric Coupling to Chiral Environments

Abstract

We show that a propagating Dirac electron with intrinsic spin generically carries a real--space helical conserved current, even in the absence of orbital angular momentum. Using exact Dirac eigenstates in cylindrical confinement, we demonstrate that this helical structure possesses definite handedness, persists into evanescent regions, and is characterized by a geometric helix pitch independent of the longitudinal de~Broglie wavelength. This intrinsic helical geometry enables a local geometric coupling between a propagating electron and a chiral environment, yielding chirality--dependent spin selectivity through current geometry rather than through a spin--orbit coupling term.
Paper Structure (5 sections, 17 equations, 1 figure)

This paper contains 5 sections, 17 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Dirac Eigenstates in Cylindrical Confinement
  3. Intrinsic Helical Current at $l=0$
  4. Helix Pitch and Local Chiral Coupling
  5. Discussion and Conclusion

Figures (1)

  • Figure 1: A propagating Dirac electron along the $+z$ direction with intrinsic spin up exhibits a helical conserved current at $l=0$. The arrow indicates the circulation direction, and the label $4Z$ marks four helix pitches. The helix represents a spatial current geometry rather than a particle trajectory. The central helical curve corresponds to the maximal azimuthal-current streamline at the characteristic radius $\rho=\rho_*$, while the surrounding shaded tube provides a visual thickness around this streamline (rendered with radius $a=0.2\,\rho_*$) and does not represent the current magnitude or radial distribution. Reversing the electron spin yields the opposite helical handedness.