  We study the Bloch spectrum and spin physics of 2D massless Dirac electrons
in single layer graphene subject to a one dimensional periodic Kronig-Penney
potential and Rashba spin-orbit coupling. The Klein paradox exposes novel
features in the band dispersion and in graphene spintronics. In particular it
is shown that: (1) The Bloch energy dispersion $\veps(p)$ has unusual
structure: There are {\it two Dirac points} at Bloch momenta $\pm p \ne 0$ and
a narrow band emerges between the wide valence and conduction bands. (2) The
charge current and the spin density vector vanish. (3) Yet, all the
non-diagonal elements of the spin current density tensor are finite and their
magnitude increases linearly with the spin-orbit strength. In particular, there
is a spin density current whose polarization is perpendicular to the graphene
plane. (4) The spin density currents are space-dependent, hence their
continuity equation includes a finite spin torque density.
