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Spin-Dependent Scattering from Gated Obstacles in Graphene Systems

This study explores the spin-dependent scattering of particles in graphene systems influenced by gated obstacles. We delve into the Hamiltonian governing the system, derived phase shifts, and analyze differential and total cross-sections as well as conductivity—a key factor tied to relaxation time. Our findings reveal conserved helicity, leading to destructive interference patterns and the Klein paradox, alongside angular anisotropy in scattering behavior. The interplay between intrinsic and Rashba spin-orbit interactions highlights phenomena such as broken spin degeneracy and preserved time-reversal symmetry in scattering processes.

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Spin-Dependent Scattering from Gated Obstacles in Graphene Systems

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  1. Spin-Dependent Scattering From Gated Obstacles in Graphene Systems M.M. Asmar& S.E. Ulloa Ohio University

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

  3. Motivation N. Tombros, C. Jozsa, M. Popinciuc, H. T. Jonkman, and B. J. van Wees, Nature (London) 448, 571 (2007).

  4. The studied system and the mathematical approach The Hamiltonian of the system • C. L. Kane and E. J. Mele, PRL 95, 226801 (2005).

  5. From the analytical form of the wave function we obtain the following quantities: • Phase shifts. • Differential cross sections. • Total cross sections which are inversely proportional to the elastic scattering time. • Transport cross section which is inversely proportional to the relaxation (transport time) time. • Conductivity, which is proportional to the relaxation time. The wave functions at the K point :

  6. A phase shift is acquired The scattering amplitude depends the acquired phase . • D. S. Novikov, PHYSICAL REVIEW B 76, 245435 2007

  7. Results and Analysis for

  8. and

  9. and

  10. and

  11. Results and Analysis for and when

  12. Conclusions • Conserved helicityDestructive interference of back scattered waves and time reversed back scattered wavesThe Klein paradox Angular anisotropy in scattering in agreement with • Intrinsic spin orbit interaction  non conserved helicity Angularly isotropic scattering. • Rashba spin orbit interaction long wavelength and small values of the gated obstacle  back scattered particle are spin flipped particles. • Broken spin degeneracy  doubling in the number of resonances. • Preserved time reversal symmetry No polarization

  13. Thank You

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