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

Abstract: 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 $φ-qz$, screw momentum $\hbar q$, and energy $\hbarΩq$. 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 $Jχ(k)$ 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 $Δ-(k,q)=0$ and $P{\rm sb}(k,q)\simeq -1$ for $Δ_+(k,q)=0$. 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.

• The paper formulates a fully quantum mechanism for CISS through quantized heliciton-mediated scattering, predicting full sideband spin polarization at resonance.
• It employs a confined Dirac electron mode with a helical conserved current interacting with screw-symmetric chiral vibrations, enabling precise energy and momentum transfer.
• The study unifies experimental CISS observations without relying on extrinsic spin–orbit effects, paving the way for chiral spintronic devices and advanced quantum sensing.

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

Summary and Context

This work formulates a dynamical and fully quantum microscopic mechanism for Chirality-Induced Spin Selectivity (CISS) based on quantized chiral excitations—termed "helicitons"—interacting with the helical conserved-current texture of a confined Dirac electron mode. By extending a prior static local selection-rule framework (Gao et al., 16 Jun 2026), the authors introduce a quantized, screw-symmetric environmental mode as an energy and momentum reservoir, which enables fully resonant, inelastic, spin-polarized electron scattering in chiral environments. The model remains strictly local and gauge-invariant, with no reliance on ad hoc spin-dependent potentials or extrinsic magnetic interactions.

The resulting theory gives a mathematically explicit expression for the spin polarization in the output channel, controlled entirely by sideband resonances associated with heliciton emission or absorption, with full reversal of polarization upon inverting the chiral handedness. The analysis provides a coherent, operator-level connection from microscopic chiral structure to macroscopic spin-selectivity in transport or scattering, and unifies several features appearing in CISS observations and phenomenological theories.

Theoretical Framework

The model is constructed in three essential stages:

• Helical Dirac Current Texture: A confined Dirac electron in a cylindrical channel, even with zero angular momentum projection ($l=0$), exhibits a helical conserved current—longitudinal and azimuthal components with opposite handedness for spin-up and spin-down—rendering the current intrinsically chiral in its spatial structure.
• Chiral Environmental Quantization (Helicitons): The environmental chirality, previously described as a static, screw-symmetric scalar potential $V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$, is promoted to a quantized oscillator, described by bosonic ladder operators $\hat{a}_q, \hat{a}_q^\dag$, with well-defined screw momentum $\hbar q$, energy $\hbar\Omega_q$, and oscillator number $n_q$. This quantized degree of freedom—the heliciton—can represent a chiral phonon, torsional vibration, or other quantized environmental screw modes.
• Heliciton-Assisted Inelastic Scattering: The coupling between the electron and heliciton sectors enables sideband creation via absorption or emission of environmental quanta, resulting in transitions:

$$|\psi_{\uparrow k}; n_q\rangle \rightarrow |\psi_{\downarrow, k+q}; n_q-1\rangle$$

$$|\psi_{\downarrow k}; n_q\rangle \rightarrow |\psi_{\uparrow, k-q}; n_q+1\rangle$$

Each process conserves total energy and samples the geometric overlap $J_\chi(k)$ between the electron’s helical current and the chiral environmental mode.

Crucially, the resonant denominators in the resulting Born-scattering amplitudes encode precise energy and momentum conservation governed by the heliciton frequency $\Omega_q$ and momentum $V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$0. No phenomenological spin–orbit coupling is introduced; the effect emerges from Dirac current geometry and environmental quantum structure alone.

Numerical Results and Key Predictions

The normalized sideband spin polarization, $V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$1, is derived as:

$V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$2

with

$V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$3

At the respective heliciton resonances ($V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$4 or $V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$5), full spin polarization is achieved in the sideband sector ($V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$6). Reversal of environmental handedness ($V_\chi(\rho,\phi,z) = V_0f(\rho)\cos(\phi-qz)$7) strictly inverts the output polarization, in direct correspondence with empirical CISS enantioreversibility signatures.

Notably, high selectivity—full polarization—emerges without any ad hoc spin filtering, extrinsic fields, or tailored interface effects, thereby distinguishing the theory from alternatives relying on interface-induced spin–orbit or magnetic coupling.

Implications, Relation to Prior Work, and Outlook

This heliciton-mediated CISS mechanism resolves several open theoretical challenges outlined in comprehensive reviews [Evers et al. 2022, Naaman & Waldeck 2015], specifically the need for a direct and physically transparent route from local chiral structure to dynamical, resonant, spin-selective scattering, robust in weak or absent intrinsic spin–orbit environments. It also unifies features observed in chiral phonon experiments [Juraschek et al. 2025, Ishito et al. 2023, Chen et al. 2022] and chiral electron vortex studies.

Practically, the model suggests that engineered quantized chiral modes—such as optically or electronically addressable helicitons—offer knobs for external control or amplification of spin selectivity, with possible ramifications for chiral spintronic devices, quantum sensing, and robust spin-current sources. The explicit dependence on well-defined quantum numbers and environmental mode occupation offers prospects for resonance-based detection and manipulation of chiral-induced spin-filtering.

Theoretically, the approach sets a blueprint for exploring CISS in more complex topologies (e.g., higher angular momentum or open geometries), multi-mode environments, and strong-coupling regimes. The strict locality and gauge invariance built into the model make it an attractive testbed for probing fundamental aspects of quantum chiral symmetry breaking in Dirac systems and their interaction with quantized lattice or molecular degrees of freedom.

Conclusion

The paper presents a quantum dynamical mechanism for chirality-induced spin selectivity via heliciton-mediated inelastic resonant scattering with a helical Dirac electron current. The theory connects local chiral geometry, quantized environmental motion, and inelastic electron scattering without invoking extrinsic spin–orbit effects or arbitrary spin-polarizing fields. Strong sideband spin polarization at resonance and strict handedness inversion constitute rigorous experimental signatures. The framework’s generality, fully operatorial nature, and direct link to chiral quantum environments have broad implications for both chiral spintronics and the theoretical foundation of CISS. Future extensions to multimode, strong-coupling, and dissipative environments are immediate directions for further theoretical and applied research.

Reference: "Heliciton-Assisted Chirality-Induced Spin Selectivity from Helical Dirac Current" (2607.00624)