We study the scattering of Dirac fermions in a sheet of graphene from potential obstacles created by external gates in the presence of both intrinsic and extrinsic spin-orbit (SO) interactions [1]. Obtaining analytical solutions in a real-space representation for the eigenvectors allows us to calculate the phase shifts generated by a finite-size obstacle in the presence of SO interactions [2]. From the phase shifts extracted from these solutions we can calculate the differential, total and transport cross sections. The knowledge of these quantities allows us to obtain the spin-flip and momentum relaxation times. The dependence of both relaxation times on the strength of the SO interaction was analyzed showing comparable relaxation times for relatively large values of energy, while displaying a big difference for small values of energy. The relaxation times of the injected electrons exhibit a number of resonances in energy associated with the structure of the scattering obstacle. In the presence of SO, new resonances appear at energies that depend on the strength of the SO interactions, and as such contain spectroscopic information on the system. It has been shown that the main scattering mechanism in graphene is due to strong defects [3]. Therefore, the analysis performed in our work can help understand the role of SO interactions in the scattering processes in these and related experiments.

[1] C. L. Kane and E. J. Mele, PRL 95, 226801 (2005).

[2] A. H. Castro Neto and F. Guinea, PRL 103, 026804 (2009).

[3] M. Monteverde, C. Ojeda-Aristizabal, R. Weil, K. Bennaceur, M. Ferrier, S. Gueron, C.Glattli, H. Bouchiat, J. N. Fuchs, and D. L. Maslov, PRL 104, 126801 (2010).