Graphene, a monoatomic layer of carbon, is perhaps the simplest and most easily available material where electrons behave as massless Dirac particles. Apart from the many promising technological applications, the study of graphene (and other layered materials) has opened a number of interesting theoretical questions: the microscopic crystalline structure requires an additional degree of freedom (the pseudo spin) that gives rise to effects such as the Klein paradox or Veselago electron lenses. The spin-orbit interaction (SOI) in materials arises from intrinsic lack of inversion symmetry in the lattice structure or from external or interfacial fields that break spatial symmetries. Although SOI is weak in natural graphene, it can be enhanced by local hybridizations with impurities by manipulation of substrates or applied gates. In this talk, I will present our theoretical studies of electronic transport [1] and Kondo screening in graphene [2] under sizeable SOI and some of the anticipated observables, including birefringence in electron optics [3].

[1] M. M. Asmar and S. E. Ulloa, Phys. Rev. Lett. 112, 136602 (2014).

[2] D. Mastrogiuseppe. A. Wong, K. Ingersent, S. E. Ulloa and N. Sandler, Phys. Rev. B 90, 035426 (2014).

[3] M. M. Asmar and S. E. Ulloa, Phys. Rev. B 87, 075420 (2013).