The chiral-induced spin selectivity (CISS) effect, which describes the spin-filtering ability of diamagnetic structures like DNA or peptides having chiral symmetry, has emerged in the past years as the central mechanism behind a number of important phenomena, like long-range biological electron transfer, enantiospecific electrocatalysis, and molecular recognition. Also, CISS-induced spin polarization has a considerable promise for new spintronic devices and the design of quantum materials. The CISS effect is attributed to spin–orbit coupling, but a sound theoretical understanding of the surprising magnitude of this effect in molecules without heavy atoms is currently lacking. We are taking an essential step into this direction by analyzing the importance of imaginary terms in the Hamiltonian as a necessary condition for non-vanishing spin polarization in helical structures. Based on first-principles calculations and analytical considerations, we perform a symmetry analysis of the key quantities determining transport probabilities of electrons of different spin orientations. These imaginary terms originate from the spin–orbit coupling, and they preserve the Hermitian nature of the Hamiltonian. Hence, they are not related to the breaking of time-reversal symmetry resulting from the fact that molecules are open systems in a junction. Our symmetry analysis helps to identify essential constraints in the theoretical description of the CISS effect. We further draw an analogy with the appearance of imaginary terms in simple models of barrier scattering, which may help understanding the unusually effective long-range electron transfer in biological systems.<br>
Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures