  Semiconductors with strong spin-orbit interactions can exhibit a helical gap
with spin-momentum locking opened by a magnetic field. Such a gap is highly
spin selective as a result of a topologically protected spin-momentum locking,
which can be used for spin filtering. We experimentally demonstrate such a spin
filtering effect in a quasi-ballistic p-type germanium/silicon core/shell
nanowire (NW), which possesses a pseudo-helical gap without the application of
magnetic field. Polarized hole spin injection to the NW is achieved using
cobalt ferromagnetic contacts with controlled natural surface oxide on the NW
as a tunnel barrier. Local and nonlocal spin valve effects are measured as the
verification of polarized spin transport in the NW outside the helical gap. We
electrically tune the NW into the helical gap by scanning its chemical
potential with a gate. A hysteresis loop with three resistance states is
observed in the local spin valve geometry, as an evidence of spin filtering in
the helical gap.
