SU(2)⊗SU(2) bi-spinor structure entanglement induced by a step potential barrier scattering in two-dimensions

The entanglement between SU(2)⊗SU(2) internal degrees of freedom of parity and helicity for reflected and transmitted waves of Dirac-like particles scattered by a potential step along an arbitrary direction on the x-y plane is quantified. Diffusion (E≥V) and Klein zone (V≥E) energy regimes are considered. It has been shown that, for SU(2)⊗SU(2) polarized structures of helicity eigenstates impinging the barrier, the local interaction with a step potential destroys the parity-spin separability. The framework presented here can be straightforwardly translated into a useful theoretical tool for obtaining the spin-spin entanglement in the context of enlarged scenarios of nonrelativistic 2D systems, as for instance those for describing single layer graphene, or even single trapped ions with Dirac bi-spinor mathematical structure.