Chiral tunneling in single layer graphene with Rashba spin-orbit coupling: spin currents

We study forward scattering of 2D massless Dirac electrons at Fermi energy {\varepsilon} > 0 in single layer graphene through a 1D rectangular barrier of height {u_0} in the presence of uniform Rashba spin-orbit coupling (of strength λ). The role of the Klein paradox in graphene spintronics is thereby exposed. It is shown that (1) For {\varepsilon} - 2λ < {u_0}< {\varepsilon} + 2λ there is partial Klein tunneling, wherein the transmission is bounded by 1 and, quite remarkably, for small λ > {λ_0} {\approx} 0.1 meV, the transmission nearly vanishes when the scattering energy equals the barrier height, {\varepsilon}={u_0}. (2) Spin density and spin-current density are shown to be remarkably different than these observables predicted in bulk single layer graphene. In particular, they are sensitive to λ and {u_0}. (3) Spin current densities are space dependent, implying the occurrence of non-zero spin torque density. Such a system may serve as a graphene based spintronic device without the use of an external magnetic field or magnetic materials.