Quantum Geometry of the Chirality Induced Spin Selectivity Effect

Chirality underpins a vast array of physical systems, providing a degree of freedom that may often be hidden in plain sight but can give rise to exotic phenomena. One such effect which has garnered growing interest is the chirality-induced spin selectivity (CISS) in which ordered films of chiral molecules act as filters for electron spin, with substantial spin-dependent charge separation being realized. In solid-state systems, topological phases of matter arise from strong spin-orbit interactions, due to electron interactions with heavy lattice ions. The CISS effect in molecules exhibits several hallmarks of topological insulators—spin-dependent transport, spin-locked states, and a nontrivial spin-orbit coupling. This reasoning is enhanced by the discovery of an orbital texture in the band structure of DNA-like molecules. As such, it seems critical to understand whether the spin-polarization from the CISS effect is due to a topologically nontrivial quantum geometry. Our approach involves examining nonrelativistic electrons moving along a helical path, under the effect of a Rashba-like spin-orbit coupling, a constant Zeeman field, and a dipole potential. Using the properties of the CISS Hamiltonian, we compute the non-abelian Berry phase and Chern number for the eigenstates of the Hamiltonian. Topological classification of chiral molecules potentially gives rise to novel exploitation of the CISS effect, expanding the developing field of spintronics into molecular materials.