Rashba spin-orbit coupling in graphene monolayer coated by periodic magnetic stripes.

We investigate theoretically the effects of a modulated periodic perpendicular magnetic fields and the Rashba spin-orbit coupling (RSOC) on the electronic states and optical absorption spectrum in a graphene monolayer. The magnetic fields and supperlattice geometry give rise to distinct Dirac cone shift and open a finite bandgap at the Dirac point. In contrast to the energy spectrum without the RSOC interaction, we find that the RSOC term will develop a spin-splitting energy-momentum dispersion relation in this graphene magnetic supperlattice. Anisotropic and spin-split group velocities, effective masses and the momentum-dependent carrier distributions along the magnetic strips are demonstrated. And the manipulations of these exotic properties by tuning the magnetic fields and the RSOC are addressed systematically. Accordingly, we find bright-to-dark transitions in the electron-hole pairs transition rate spectrum and absorption peak splitting in the optical absorption spectrum tuned by the RSOC interaction. This feature offers us a practical way to detect these band engineering effects especially the exotic spin splitting states by using the conductance and optical technique.