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This paper resolves the long-standing debate on the origin of Chirality-Induced Spin Selectivity (CISS) by establishing a single exact rule: CISS is a time-reversal odd, non-equilibrium effect in nonmagnetic, time-reversal-invariant conductors. Evaluating leading theoretical mechanisms across four levels of nonequilibrium transport, the study verifies this rule and demonstrates that coherent chiral vibrations are the primary driver, generating substantial collinear polarization that reverses with handedness. The findings reveal CISS acts as both a spin polarizer and a weaker spin filter, with polarization scaling with effective spin-orbit coupling and exhibiting trends consistent with biological molecules.
Chirality alone is insufficient for CISS; the effect fundamentally requires nonequilibrium conditions and time-reversal odd dynamics, with coherent vibrations driving substantial spin polarization.
For two decades, the origin of Chirality-Induced Spin Selectivity (CISS), the spin polarization of electrons by nonmagnetic chiral systems without magnetic fields, has remained unsettled. Here, we establish a single exact rule defining the fundamental conditions for the effect: in nonmagnetic, time-reversal-invariant conductors, all measurable CISS signals are time-reversal odd and vanish near equilibrium, proving that structural chirality alone is insufficient. By evaluating leading theoretical mechanisms across four levels of nonequilibrium transport, from coherent classical driving to fully non-Markovian quantum baths, we verify this selection rule to machine precision. We show that coherent chiral vibrations generate substantial collinear polarization (up to 10 percent across 0.5-6 THz) that reverses with handedness, whereas incoherent vibrations yield under 1 percent, and non-Markovian bath memory further suppresses the signal. The chiral geometry first makes the electronic motion chiral by accumulating orbital angular momentum; spin-orbit coupling (SOC) then converts that into spin. CISS therefore acts as both a spin polarizer and a spin filter, the latter an order of magnitude weaker. The polarization grows with molecular length and then saturates, matching trends reported for DNA and peptides. Reversing the drive converts decaying spin into a handedness-locked charge-current pulse (inverse-CISS). We find that once the system is driven, the polarization magnitude scales with an effective spin-orbit coupling: making heavy atoms and curved light-atom backbones indistinguishable at equivalent effective SOC. This enables us to chart how geometry, driving field, and length separate those routes.