Explanation of the Diagram of the Rashba Effect

Main Question or Discussion Point

Hello,

I find something about the Rashba Spin Orbit coupling but im not sure how to understand it. Hope you can help me. Consider the following picture of the Rashba effect i found:
Rashba.png


Well i dont really know whats about the arrows here. They should showing the spin direction i guess but i dont see there meaning.
Can somebody help how to interprete this diagram??
 

Answers and Replies

TeethWhitener
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The ##k_x## vs. ##k_y## plot is just a slice through the ##E(\mathbf{k})## vs. ##\mathbf{k}## plot at constant ##|\mathbf{k}|##. Basically, imagine rotating the right-hand diagram about the ##E(k)## axis and slicing through ##E = 0##. The arrows simply show that the spins become momentum-dependent. The inner ring has opposite spins from the outer ring, but the spin projections are going to depend on where along those rings you are in momentum space.
 
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At the risk of casting more confusion on the topic, I found this picture, https://www.physics.harvard.edu/node/549, which seems to contradict your picture. Harvard's picture make more sense to me:-)
 
TeethWhitener
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I don't see the contradiction. b and e are literally the same pictures as OP. Only the arrows are different colors.
 
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The issue I have with the OP's diagram is with the right hand picture of the two horizontally displaced parabolas. Each parabola has spin up or spin down. Call the right most parabola blue with it's electron in the down state, then the left parabola has its red electron in spin up state. So starting from the right hand side of the diagram I would expect blue (down), then red (up), then blue (down) and finally red (up). I think that this would demonstrate that the electron (or hole) hops from one lattice site to a neighboring site in a two stage process. Since we are considering surface states, it suffers a spin orbit interaction, from the bulk, with its surface neighbor causing it to hop, then flips its spin because the z component of momentum is suppressed.
 

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