  Chirality-induced spin selectivity (CISS) refers to the fact that electrons
get spin polarized after passing through organic chiral molecules in a
nanoscale device. In CISS, chiral molecules are commonly believed to be a spin
filter through which one favored spin transmits and the opposite spin gets
reflected, i.e., transmitted and reflected electrons exhibit opposite spin
polarization. In this work, we point out that such a spin filter scenario
contradicts the principle that equilibrium spin current must vanish. Instead,
we find that both transmitted and reflected electrons present the same type
spin polarization, which is actually ubiquitous for a two-terminal device. More
accurately, chiral molecules play the role of a spin polarizer rather than a
spin filter. The direction of spin polarization is determined by the molecule
chirality and the electron incident direction. And the magnitude of spin
polarization replies on local spin-orbit coupling in the device. Our work
brings a deeper understanding on CISS and interprets recent experiments, for
example, the CISS-driven anomalous Hall effect.
