  Spin-orbit coupling gives rise to a range of spin-charge interconversion
phenomena in non-magnetic systems where certain spatial symmetries are reduced
or absent. Chirality-induced spin selectivity (CISS), a term that generically
refers to a spin-dependent electron transfer in non-magnetic chiral systems, is
one such case, appearing in a variety of seemingly unrelated situations ranging
from inorganic materials to molecular devices. In particular, the origin of
CISS in molecular junctions is a matter of an intense current debate. Here we
derive a set of geometrical conditions for this effect to appear, hinting at
the fundamental role of symmetries beyond otherwise relevant quantitative
issues. Our approach, which draws on the use of point-group symmetries within
the scattering formalism for transport, shows that electrode symmetries are as
important as those of the molecule when it comes to the emergence of a
spin-polarization and, by extension, to the possible appearance of CISS. It
turns out that standalone metallic nanocontacts can exhibit spin-polarization
when relative rotations which reduce the symmetry are introduced. As a
corollary, molecular junctions with $\textbf{achiral}$ molecules can also
exhibit spin-polarization along the direction of transport, provided that the
whole junction is chiral in a specific way. This formalism also allows the
prediction of qualitative changes of the spin-polarization upon substitution of
a chiral molecule in the junction with its enantiomeric partner. Quantum
transport calculations based on density functional theory corroborate all of
our predictions and provide further quantitative insight within the
single-particle framework.
