Undergrad How Does Spin Hall Effect Couple Charge and Spin Current?

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The discussion centers on understanding the Spin Hall Effect and how spin-orbit interaction couples charge and spin currents. The Spin Hall Effect arises from a scattering potential that combines Coulomb and spin-orbit potentials, leading to spin polarization of the scattered current. This polarization exhibits asymmetry relative to the transverse direction of the charge current. A referenced paper by Jorge Hirsch is suggested as a resource for further clarification. Overall, the interaction is essential for comprehending the coupling of charge and spin currents in this phenomenon.
semc
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Hi,

I have been trying to understand how the spin hall effect comes about. However, everywhere I look I just find 'the spin-orbit interaction couples the charge and spin current'. I really don't understand how does the current couple through the interaction. Any help would be much appreciated.

Thanks!
 
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I think this paper by Jorge Hirsch will shed some light on your question; https://arxiv.org/pdf/cond-mat/9906160.pdf. The spin-orbit interaction couples to the spin current by a scattering potential which is the sum of a Coulomb potential and a spin-orbit potential. The scattered current becomes spin polarized with asymmetry with respect to the direction transverse to the charge current direction.

Peace,
Fred
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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