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

Abstract

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 $φ-qz$, longitudinal momentum $\hbar q$, and energy $\hbarΩ_q$. 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 $\mathcal J_χ(k)$ but differ in ladder factors, final momenta, and detunings. With spectral factors $\mathcal S_+$ and $\mathcal S_-$, $P_{\rm sb}=[\mathcal S_--\mathcal O(T)\mathcal S_+]/ [\mathcal S_-+\mathcal O(T)\mathcal S_+]$, where $\mathcal O(T)=\exp[-\hbarΩ_q/(k_BT)]$. An isolated emission or absorption resonance yields $P_{\rm sb}\simeq+1$ 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 $P_{\rm sb}$ 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-$Ω_q$ 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.