  We present a novel fundamental effect that for the matter waves the
space-averaging free-fall point of quantum particles undergoes a spin-dependent
transverse shift in the gravitational field of Earth. This effect is similar to
the geometric spin Hall effect (GSHE) [Aiello et al., Phys. Rev. Lett. 103,
100401 (2009)] and can be called gravity-induced GSHE. This effect suggests
that there might be violations of the universality of free fall (UFF) or weak
equivalence principle (WEP) in the quantum domain.
