Electrical Manipulation of Spin-Dependent Anisotropy of a Dirac Cone in a Graphene Superlattice with Alternating Periodic Electrostatic and Exchange Fields

We studied the spin-dependent behavior of the electronic properties of alternating periodic potentials applied to finite and infinite graphene superlattices coupled with tunable electrostatic and exchange fields. The band structures were evaluated using the transfer matrix approach. The results of tuning the coupled electrostatic potential and exchange field showed that the spin-dependent anisotropy of a Dirac cone depends on the difference between the amplitude of periodically modulated coupling. Spin-dependent collimation occurs when the modulations become zero-average potentials with the ratio of both periodically modulated strengths equals one, in which one spin can be moved freely, but the other one is highly collimated. In addition, we find that the number of extra Dirac points in the infinite superlattice is spin-dependent. In terms of spin-ups, their number increases with an increase in the strength of both modulated fields. To ensure this calculation, we also compute the conductance of finite periodic modulation at zero energy. It is shown that the peaks of the conductance occur when the extra Dirac point emerges. This result may be utilized to design graphene-based devices with highly spin-polarized collimators.