Helical Dirac Current with Local Coupling to a Chiral Potential

• URL: http://arxiv.org/abs/2606.17618v1
• Date: Tue, 16 Jun 2026 07:24:37 GMT
• Title: Helical Dirac Current with Local Coupling to a Chiral Potential
• Abstract summary: We show that exact Dirac eigenstates in cylindrical confinement carry a definite helical conserved-current texture.<n>For the lowest confined mode, the Dirac current contains a nonvanishing azimuthal component together with longitudinal transport.
• Score: 1.9879064696481736
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that exact Dirac eigenstates in cylindrical confinement carry a definite helical conserved-current texture even in the zero orbital angular momentum channel l = 0. For the lowest confined mode, the Dirac current contains a nonvanishing azimuthal component together with longitudinal transport and exhibits opposite handedness in the two spin-resolved sectors. The structure also persists into the evanescent region. We further derive the channel-resolved matrix-element kernel generated by a static chiral scalar potential acting on the confined l = 0 Dirac modes. The resulting spin-selective coupling arises from the Dirac current texture and the scalar chiral potential, and yields a geometric selection rule in which diagonal channels vanish while off-diagonal conversion channels survive. The coupling strength is governed by an internal sampled-current overlap Jchi(k), defined as the integral from 0 to R of f(rho) times jphi_up(rho, k) times rho d rho. This quantity measures the spatial overlap between the chiral radial profile and the spin-up azimuthal Dirac-current density. The mechanism is fully local and texture-based, without external magnetic fields or spin-orbit coupling. Within standard Dirac theory, this work identifies the minimal static Dirac-geometric kernel underlying spin-selective response, establishing a baseline structure from which dynamical-medium, scattering, and transport formalisms can be systematically developed toward a complete description of spin-polarization phenomena such as CISS.

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