Mesoscopic spin Hall effect.

@article{Bardarson2006MesoscopicSH,
  title={Mesoscopic spin Hall effect.},
  author={Jens H. Bardarson and Inanç Adagideli and Philippe Jacquod},
  journal={Physical review letters},
  year={2006},
  volume={98 19},
  pages={
          196601
        }
}
We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is short compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average. 

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