  In the last decade, chirality-induced spin selectivity (CISS) has been
attracting extensive interest. However, there still exists a large gap between
experiments and quantitative theoretical results, and the microscopic mechanism
of CISS, especially transverse CISS where electrons are injected perpendicular
to the helix axis of chiral molecules, remains elusive. Here, we address these
issues by performing a combined experimental and theoretical study on
conducting polyaniline helical nanofibers which are synthesized in the absence
of any chiral species. Large spin polarization is measured in both left- and
right-handed nanofibers for electrons injected perpendicular to their helix
axis, which is comparable to the value of parallel electron injection in other
chiral molecules, and it will be reversed by switching the handedness between
two enantiomers. We develop a theoretical model with extremely weak spin-orbit
coupling arising exclusively from electron propagation between neighboring
polyanilines and the numerical results are quantitatively consistent with the
experimental data. Our results demonstrate that the supramolecular handedness
is sufficient for spin-selective electron transmission in chiral molecules
assembled from achiral monomers and the mechanism of transverse CISS is
revealed.
