Heliciton-Assisted Chirality-Induced Spin Selectivity from Helical Dirac Current

We develop a quantized chiral-field mechanism for chirality-induced spin selectivity (CISS). The corresponding quantum is a heliciton: a helical mode with phase coordinate $\phi-qz$, screw momentum $\hbar q$, and energy $\hbar\Omega_q$. A helical electron can absorb or emit this quantum, converting the static chiral vertex developed in our preceding work into an inelastic resonant scattering process. Using first Born scattering theory, we show that an incident two-spin-channel state generates two heliciton-assisted sidebands. Absorption converts the $\uparrow k$ channel into the $\downarrow,k+q$ sideband, while emission converts the $\downarrow k$ channel into the $\uparrow,k-q$ sideband. Thus the heliciton supplies both the screw momentum and energy needed to turn the handedness-conversion into a resonant spin-selective channel. The two sidebands inherit the same sampled-current overlap $J_\chi(k)$ from the static theory, but acquire different kinematic weights and different resonance detunings. The sideband sector reaches full spin polarization at the respective isolated heliciton resonances, with $P_{\rm sb}(k,q)\simeq +1$ for $\Delta_-(k,q)=0$ and $P_{\rm sb}(k,q)\simeq -1$ for $\Delta_+(k,q)=0$. Reversing the screw handedness, $q\rightarrow -q$, interchanges the two sideband channels and reverses the polarization. No ad hoc spin-dependent potential is introduced. The spin selectivity comes from three ingredients: helical Dirac-current texture, quantized screw-symmetric environmental motion, and resonant exchange of screw momentum and energy. This identifies CISS as a heliciton-assisted resonance mechanism that produces spin polarization in the inelastic sideband sector.