  We demonstrate that an important quantum material WTe$_2$ exhibits a new type
of geometry-induced spin-filtering effect in photoemission, stemming from low
symmetry that is responsible for its exotic transport properties. Through the
laser-driven spin-polarized angle-resolved photoemission Fermi surface mapping,
we showcase highly asymmetric spin textures of electrons photoemitted from the
surface states of WTe$_2$. Such asymmetries are not present in the initial
state spin textures, which are bound by the time-reversal and crystal lattice
mirror plane symmetries. The findings are reproduced qualitatively by
theoretical modeling within the one-step model photoemission formalism. The
effect could be understood within the free-electron final state model as an
interference due to emission from different atomic sites. The observed effect
is a manifestation of time-reversal symmetry breaking of the initial state in
the photoemission process, and as such it cannot be eliminated, but only its
magnitude influenced, by special experimental geometries.
