Theory of Chirality-Induced Spin Selectivity in Trefoil-knot Molecules

Abstract

The origin of chirality-induced spin selectivity (CISS) remains elusive, and ultrahigh spin polarization (SP) in topologically knotted molecules is unexplained. We develop a discrete geometric spin-orbit coupling (SOC) framework for molecular junctions, resolving site-specific curvature and current-partition effects beyond continuous models. For trefoil-knot molecules, it quantifies site-resolved geometric SOC, reaching $\sim$120 meV, nearly two orders of magnitude larger than intrinsic SOC of light atoms. The substrate-coupled benzene unit, carrying the largest current and remarkable geometric SOC, dominates the CISS effect. The framework quantitatively reproduces measured SP, temperature-dependent magnetoresistance (MR) and $Δ$MR trends, establishing discrete geometric SOC as a predictive tool for CISS in topologically knotted molecules.