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Spatial correlations in chaotic nanoscale systems with spin-orbit coupling

Spatial correlations in chaotic nanoscale systems with spin-orbit coupling. Anh Ngo 1 , Eugene Kim 2 and Sergio Ulloa 1. 1 Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio. USA.

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Spatial correlations in chaotic nanoscale systems with spin-orbit coupling

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  1. Spatial correlations in chaotic nanoscale systems with spin-orbit coupling Anh Ngo 1, Eugene Kim2and Sergio Ulloa1 1Department of Physics and Astronomy, and Nanoscale and Quantum Phenomena Institute, Ohio University, Athens, Ohio. USA. 2Department of Physics, University of Windsor, Windsor, Ontario, Canada N9B 3P4. Supported by NSF-DMR WMN

  2. Motivations QPC Vg1 Vg2 Fluctuations and spatial correlations of wave functions ~ J.A. Folk, et al. PRL, 76, 1699 (1996) and A. M. Chang, et al. PRL, 76,1695, (1996).

  3. Theoretical model Random matrix  Universal quantities Microscopic Model for Chaotic Nanoscale Systems Anh Ngo, Eugene Kim and Sergio Ulloa, Submitted (arXiv:1103.3265).

  4. Random matrix ensembles

  5. Anh Ngo, Eugene Kim and Sergio Ulloa, Submitted (arXiv:1103.3265).

  6. GSE Large SOC GOE-GSE Small SOC GOE Stadium billiard

  7. One point function Ais the area of the system

  8. The amplitude correlation Ais the area of the system GOE GSE

  9. Two point correlation function for up and down spin Crossover regime The same point in space R=0 

  10. Spin up and spin down Spin up and spin down become decorrelated

  11. Summary • We investigate the statistical properties of wave functions in two-dimensional • chaotic nanostructures with spin-orbit interactions and magnetic fields. • We present results for the evolution of the wave function statistics as a function • of the parameter regimes. • Weak spin-orbit coupling is expected to have consequences for spin-polarized • tunneling. • Numerical calculations for a chaotic stadium billiard are compared with • analytic results from random matrix theory. Thank you very much!

  12. Spatial correlation of chaotic eigenfunctions GSE GOE

  13. One point function General one-point function is for the GOE-GUE crossover GOE GUE GSE

  14. GOE GUE GSE Anh Ngo, Eugene Kim and Sergio Ulloa, Submitted.

  15. Coral’s wall potential : Heller, et. al. Nature 369, 464 Anh Ngo, Eugene Kim and Sergio Ulloa ‘s calculations

  16. Boundary wall :

  17. One point function GUE Anh Ngo, Eugene Kim and Sergio Ulloa, Submitted.

  18. Gaussian symplectic ensemble (GSE)

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