Spin accumulation due to Rashba-Edelstein effect

[semc]

TL;DR Summary

How to see spin accumulation due to Rashba-Edelstein effect from band diagram

I am trying to understand how do we see the spin accumulation due to Rashba-Edelstein effect. I mean everywhere I look people just say a shift in the bands due to e-field which results in spin accumulation in the transverse direction (y in this case) as shown

Can somebody explain how to see that? If we talk about the blue circle for example, I would say more up spin with +ve k than -ve k so there will be more spin up accumulation in the positive x direction. Is this wrong? Why would there be any change in y?

I would also like to check if the spin of the electrons should be rotated as the band is shifted

If spin-momentum locking is still present (which it should be), the spins should be rotated since the k values are changed?

 

[BigJDubs]

The spin accumulation due to the Rashba-Edelstein effect occurs as a result of the electric field applied to the material. When the electric field is applied, it causes a shift in the energy bands, resulting in an asymmetry in the band structure. This asymmetry leads to a difference in the spin-orbit interaction between the two bands, resulting in a net spin polarization of the electrons. This is what is referred to as the Rashba-Edelstein effect.As for your questions about the blue circle, you are correct that there will be more up spin with +ve k than -ve k, and this will lead to spin accumulation in the positive x direction. However, the spin accumulation in the y direction will come from the fact that the spins of the electrons in the different energy bands will be rotated due to the spin-momentum locking. This is because, as the electric field shifts the bands, the k-values associated with each band will be changed, which will cause the spins of the electrons in the different bands to rotate. This rotation of the spins will result in a net spin polarization in the y direction.