  The quantum transmission problem for a particle moving in a quantum point
contact in the presence of a Rashba spin-orbit interaction and applied magnetic
field is solved semiclassically. A strong Rashba interaction and parallel
magnetic field form emergent Dirac states at the center of the constriction,
leading to the appearance of resonances which carry spin current and become
bound at high magnetic fields. These states can be controlled in situ by
modulation of external electric and magnetic fields, and can be used to turn
the channel into a spin pump which operates at zero bias. It is shown that this
effect is currently experimentally accessible in $p$-type quantum point
contacts.
