  Interacting one-dimensional conductors with Rashba spin-orbit coupling are
shown to exhibit a spin-selective Peierls-type transition into a mixed
spin-charge-density-wave state. The transition leads to a gap for one-half of
the conducting modes, which is strongly enhanced by electron-electron
interactions. The other half of the modes remains in a strongly renormalized
gapless state and conducts opposite spins in opposite directions, thus
providing a perfect spin filter. The transition is driven by magnetic field and
by spin-orbit interactions. As an example we show for semiconducting quantum
wires and carbon nanotubes that the gap induced by weak magnetic fields or
intrinsic spin-orbit interactions can get renormalized by 1 order of magnitude
up to 10 - 30 K.
