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We study the Bloch spectrum and spin physics of 2D massless Dirac electronsin single layer graphene subject to a one dimensional periodic Kronig-Penneypotential and Rashba spin-orbit coupling. The Klein paradox exposes novelfeatures in the band dispersion and in graphene spintronics. In particular itis shown that: (1) The Bloch energy dispersion $\veps(p)$ has unusualstructure: There are {\it two Dirac points} at Bloch momenta $\pm p \ne 0$ anda narrow band emerges between the wide valence and conduction bands. (2) Thecharge current and the spin density vector vanish. (3) Yet, all thenon-diagonal elements of the spin current density tensor are finite and theirmagnitude increases linearly with the spin-orbit strength. In particular, thereis a spin density current whose polarization is perpendicular to the grapheneplane. (4) The spin density currents are space-dependent, hence theircontinuity equation includes a finite spin torque density.

Chiral Bloch states in single layer graphene with Rashba spin-orbit coupling: Spectrum and spin current density