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

We develop a quantized screw-mode mechanism for chirality-induced spin selectivity (CISS). The corresponding quantum, termed a heliciton, is a screw-symmetric environmental excitation with phase $\phi -qz$, longitudinal momentum $\mathrm{\hslash }q$, and energy $\mathrm{\hslash }{\mathrm{\Omega }}_q$. Its absorption and emission convert the static local chiral vertex developed in our preceding work into an inelastic resonant scattering process. In first Born approximation, absorption maps $\uparrow ,k$ to the $\downarrow ,k+q$ sideband, whereas emission maps $\downarrow ,k$ to the $\uparrow ,k-q$ sideband. The two outputs share the sampled-current overlap ${\mathcal{J}}_{\chi }(k)$ but differ in ladder factors, final momenta, and detunings. With spectral factors ${\mathcal{S}}_{+}$ and ${\mathcal{S}}_{-}$, $P_{\mathrm{s}\mathrm{b}}=[{\mathcal{S}}_{-}-\mathcal{O}(T){\mathcal{S}}_{+}]\mathrm{/}[{\mathcal{S}}_{-}+\mathcal{O}(T){\mathcal{S}}_{+}]$, where $\mathcal{O}(T)=\exp [-\mathrm{\hslash }{\mathrm{\Omega }}_q\mathrm{/}(k_{B}T)]$. An isolated emission or absorption resonance yields $P_{\mathrm{s}\mathrm{b}}\simeq +1$ or $-1$, respectively, in the resolved sideband sector. Reversing the screw handedness interchanges the spin identities of the two sidebands while leaving their spectral and occupation weights unchanged, and therefore reverses $P_{\mathrm{s}\mathrm{b}}$ at every temperature. At high temperature, absorption and emission have nearly equal occupation weights; at low temperature, absorption is exponentially suppressed while spontaneous emission remains. Liquid-nitrogen temperature can already produce a pronounced asymmetry for higher-${\mathrm{\Omega }}_q$ modes. Thus a spatially resolved Dirac wave with spin-dependent helical conserved current couples locally to a heliciton and produces thermally weighted spin- and momentum-resolved sidebands without an ad hoc spin-dependent potential.