K dot p method with SO interaction

In summary, the conversation is about deriving the k dot p formula with the spin orbit interaction term included. The speaker is having trouble handling the cross product term from the SO and understanding the effect of the Pauli matrix vector on the spinor. They also mention the issue of letting p act on the Bloch states to derive the correct formula. The desired result is attached, and the speaker has written up their progress so far. The problem is described as a degenerate perturbation theory and the suggestion is made to first try to diagonalize the sigma matrices.
  • #1
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I am trying to derive the k dot p formula with the spin orbit interaction term included. I am having some trouble. I insert a bloch wave function multiplied with an unspecified spinor. But how do I treat the cross product term that comes from the SO and what is the effect of the pauli matrix vector on the spinor? And also: Since the spin orbit term contain the gradient of the coulomb potential how can I let p act on the bloch states? (I assume this how you derive the correct formula?)
The result I want is the attached. Also I attached what I have written up so far.
 

Attachments

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  • #3
This is a problem of degenerate perturbation theory. I would first try to diagonalize the sigma matrices.
 

Related to K dot p method with SO interaction

1. What is the K dot p method with SO interaction?

The K dot p method with SO interaction is a theoretical approach used in condensed matter physics to study the electronic properties of materials. It combines the K dot p method, which is a perturbative method for calculating the electronic band structure, with the spin-orbit interaction, which is a relativistic effect that arises from the interaction between the spin of the electron and its motion.

2. How does the K dot p method with SO interaction differ from the regular K dot p method?

The regular K dot p method only takes into account the kinetic energy of the electrons, while the K dot p method with SO interaction also includes the effects of spin-orbit coupling. This allows for a more accurate description of the electronic band structure, particularly for materials with heavy elements or strong spin-orbit interactions.

3. What are the advantages of using the K dot p method with SO interaction?

One of the main advantages of using the K dot p method with SO interaction is that it can accurately describe the electronic band structure of materials with strong spin-orbit coupling. It is also a computationally efficient method, making it useful for studying large systems or systems with complex crystal structures. Additionally, it can provide insight into the spin properties of the electrons in a material.

4. What are some applications of the K dot p method with SO interaction?

The K dot p method with SO interaction has a wide range of applications in condensed matter physics. It is commonly used to study the electronic properties of semiconductors, topological insulators, and spintronic materials. It can also be applied to the design and optimization of electronic devices, such as transistors and quantum dots.

5. Are there any limitations to the K dot p method with SO interaction?

Like any theoretical method, the K dot p method with SO interaction has its limitations. It may not accurately describe materials with very complex electronic structures or materials with strong electron-electron interactions. Additionally, it assumes a single-band model, so it may not be suitable for materials with multiple bands crossing at the Fermi level.

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