1. M.M. Asmar & S.E. Ulloa Ohio University

2. Outline Motivation. The studied system and the mathematical approach. Results and analysis. Conclusions.

3. Because of the high importance of the field spintronics on which the spin orbit interactions play a basic role, we study and compare the relaxation times in the presence of a gated potential to the relaxation times in the presence of SOI in graphene systems. The importance of the relaxation times is based on their proportionality to the conductance of the system. Motivation

4. The studied system and the mathematical approach The Hamiltonian of the system:

5. Wave functions (at K point) are :, and From the analytical form of the wave function we can extract some information such as Phase shifts Differential cross sections Total cross sections Transport cross section which is inversely proportional to the relaxation time Conductance, which is proportional to the relaxation time Total angular momentum C. L. Kane and E. J. Mele, PRL 95, 226801 (2005).

6. Results and Analysis In the presence of a gated obstacle and no SOI Ramsauer-Townsend Effect at V/ 2 J. Milton Pereira, Jr., V. Mlinar, and F. M. Peeter, P RB 74, 045424 (2006)

7. In the presence gated obstacles and Intrinsic SOI C. L. Kane and E. J. Mele, PRL 95, 226801 (2005). Daniel Huertas-Hernando, F. Guinea,and Arne Brataas1, PRB 74, 155426 (2006).

8. In the presence of the gated obstacle and Rashba SOI Comparable relaxation times Gierz, et al., arXiv:1004.1573. J. Sánchez-Barriga, et al., Diamond & Related Materials 19 (2010) 734–74

9. Longer spin flip relaxation times A.H. Castro Neto and F. Guinea, PRL 103, 026804 (2009). N. Tombros et al., Nature (London) 448, 571 (2007).

10. In the presence of the gated obstacle RSOI and ISOI

11. Conclusions Quasi bound states reflect themselves as resonances in the cross section. ISO decrease the scattering time and shifts the resonances in the cross section. Spin flip relaxation times are much larger that the momentum relaxation times at low energy of electrons. Momentum and spin flip scattering times are comparable at relatively high energies of electrons. Spin flip times and momentum relaxation times are equal at both the K and K’ point.