# Explanation of the Diagram of the Rashba Effect

• A
• JanSpintronics
In summary, the Rashba Spin Orbit coupling is a phenomenon that results from the electron (or hole) hopping between lattice sites.
JanSpintronics
Hello,

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

Well i don't really know what's about the arrows here. They should showing the spin direction i guess but i don't see there meaning.
Can somebody help how to interprete this diagram??

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.

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:-)

I don't see the contradiction. b and e are literally the same pictures as OP. Only the arrows are different colors.

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.

## 1. What is the Rashba Effect?

The Rashba Effect is a phenomenon in condensed matter physics where an electric field applied to a material causes the spin of electrons to split, resulting in a net spin polarization.

## 2. How does the Rashba Effect work?

The Rashba Effect is caused by the spin-orbit interaction, where the spin of an electron is coupled with its motion. When an electric field is applied, it creates an asymmetric potential that affects the motion of the electrons and causes their spins to split.

## 3. What is the significance of the Rashba Effect?

The Rashba Effect has important implications in spintronics, a field that aims to use the spin of electrons for information processing and storage. It also plays a crucial role in the development of new materials for electronic devices.

## 4. How is the Rashba Effect represented in a diagram?

The Rashba Effect is typically represented in a band structure diagram, where the energy levels of electrons are plotted against their wave vectors. The spin-splitting caused by the Rashba Effect can be seen as a splitting of the energy bands in the diagram.

## 5. Can the Rashba Effect be observed in all materials?

No, the Rashba Effect is most commonly observed in materials with a strong spin-orbit coupling, such as semiconductors and metals with heavy elements. It is also dependent on the strength of the applied electric field.

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