Relativistic Dynamics and Electron Transport in Isolated Chiral Molecules

The Chirality-Induced Spin Selectivity (CISS) effect describes the ability of chiral molecules and crystals to transmit spin-polarized currents, a phenomenon first identified in 1999. Although this effect holds great promise for a broad spectrum of different applications in device physics and synthetic chemistry (including, e.g., spintronics, quantum computing, spin- and enantio-selective chemistry), its underlying mechanisms remain incompletely understood. The prevailing hypothesis attributes the CISS effect to enhanced spin-orbit coupling (SOC) within chiral molecules. However, the SOC magnitude required to align with experimental observations significantly exceeds the values derived from conventional atomic-scale calculations, particularly for systems composed of light atoms. In this work, we leverage the implementation of \texttt{fully relativistic density functional theory (DFT)} equations, as available in the \texttt{Dirac code}, to investigate how molecular chirality manifests itself in the chirality density of electronic states. We further explore how this responds to an applied external electric field. To assess spin-dependent transport, we employ the \texttt{Landauer-Imry-B\"uttiker} formalism, examining the dependence of spin transmission on the twist angle of the molecular structure that defines its geometrical chirality. While our findings qualitatively align with experimental trends, they point to the necessity of a more general treatment of SOC, \textit{e.g.}, including geometrical terms or through the dependence of advanced exchange-correlation functionals on the electronic spin-current density.