Abstract

An important element on the dynamics of spins in materials is the spin-orbit interaction (SOI), which reflects/arises from intrinsic lack of inversion symmetry in the lattice structure, or via broken symmetries in the system due to external or interfacial fields (Rashba interaction). Although intrinsic SOI is weak in graphene, the Rashba SOI can in fact be large due to strong local hybridizations by impurities of defects or by manipulation of substrates or applied gates [1]. We have studied electron/hole transport in graphene under sizeable SOI and address theoretically some of the anticipated observables due to this effect.

We have developed analytical spinor solutions of the Dirac equation that include spin dependent observables, and use these to examine the role of SOI on scattering cross sections. By calculating the ratio of total to transport cross section at low energy we are able to probe the degree of isotropy of the scattering processes, and consequently probe the nature of the impurities and defects present in the graphene sample. This suggests then a sample specific measurement of the important effective size of the SOI , especially if one is to consider spin transport.

We also show that Rashba SOI in graphene gives rise to optical birefringence in electron optics, which in essence reflects the intrinsic crystal structure even at long electronic wavelengths. This effect requires the presence of Rashba SOI , where different group velocities depend on the chirality of the electronic states, mimicking the light polarization dependence of the group velocities in optical birefringent materials. In circular “Veselago lenses” the birefringence would be evident by the doubling of caustics and cusps produced, which could be probed in scanning probe experiments.

[1] D. Marchenko et al., Nature Commun. 3, 1232 (2012). [2] M. M. Asmar and S. E. Ulloa, Phys. Rev. B 87 , 075420 (2013).