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 nonvanishing spin polarization in helical structures.
On the basis of 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.