Minimal Model for Chirally Induced Spin Selectivity: Spin-orbit coupling, tunneling and decoherence

Chirally Induced Spin Selectivity (CISS) is a transport phenomenon observed in both linear and non-linear regimes, where the spin-orbit coupling (SOC) acts as the key driver and electron tunneling serves as the dominant mechanism for charge transfer. Despite SOC's inherent time-reversal symmetry (TRS) preservation, conventional reciprocity relations limit spin polarization and the differential treatment of spin species. In experimental systems, an additional factor, spin-independent decoherence, disrupts TRS and reciprocity. We introduce decoherence using the Buttiker voltage probe within the scattering matrix framework. Our results reveal the importance of under-the-barrier decoherence as an order-of-magnitude polarization enhancement mechanism. Polarization arises by the disruption of spin precession around the spin-orbit magnetic field with a new spin component along the field direction. The alignment of polarization depends on interference effects produced by the voltage probe. We discuss the connection of our model to a more realistic decoherence mechanism in molecular systems.