Weaknesses of Fock-Darwin model

[ordinary_girl]

Hi All

I try to analyse the data of quantum dot photoluminescence in the presence of magnetic field. I have a few questions in my mind:

1. What is the weakness of Fock-Darwin (FD) model? Seems to me is fine because the result from the experiment shows the criss-cross pattern.
2. What is the original equation of energy eigenvalues in FD model?
3. Does it right the FD neglecting spin splitting? If yes, why we can observed the Landau level by plotting the graph energy vs magnetic field? From my understanding, Landau level shows the quantization energy of charged particle. So, it must take the spin splitting into account.

Is anyone here knows where I can refer the basic theory of Fock-Darwin model?
I found Fock's paper but it isn't in English.

Thank you.

 

[eljose79]

Hi there,

It's great to see that you are working on quantum dot photoluminescence in the presence of a magnetic field. This is a very interesting and complex topic in the field of quantum physics. I will do my best to answer your questions and provide some resources for further reading.

1. The Fock-Darwin model is a simplified model that neglects many important factors such as electron-electron interactions, spin-orbit coupling, and the effects of disorder. This can lead to discrepancies between the theoretical predictions and experimental results. Additionally, the model assumes a perfect circular symmetry, which may not always be the case in real quantum dot systems. However, despite these weaknesses, the Fock-Darwin model is still a useful tool for understanding the basic physics of quantum dots in a magnetic field.

2. The original equation for the energy eigenvalues in the Fock-Darwin model is given by:

E(n,m) = ℏω(n + 1/2) + ℏω_c(m + 1/2)

where n and m are the radial and angular quantum numbers, ω is the radial confinement frequency, and ω_c is the cyclotron frequency.

3. The Fock-Darwin model does indeed neglect spin splitting. However, this does not mean that the Landau levels cannot be observed in experiments. The spin splitting is typically much smaller than the energy spacing between Landau levels, so it can be neglected in most cases. However, if the magnetic field is strong enough, the spin splitting may become significant and should be taken into account.

If you are looking for more resources on the Fock-Darwin model, I would suggest checking out the book "Quantum Dots: Fundamentals, Applications, and Frontiers" by Peter Michler. It provides a comprehensive overview of the theory and applications of quantum dots, including the Fock-Darwin model.

I hope this helps answer your questions. Good luck with your research!

 

[Entropia]

Hi there,

The Fock-Darwin model is a widely used theoretical model for describing the behavior of electrons in a magnetic field, particularly in quantum dots. However, like all models, it has its limitations and weaknesses. One of the main weaknesses is that it neglects the effect of electron-electron interactions, which can be significant in certain systems. This can lead to discrepancies between the model predictions and experimental results, as you have noticed in your photoluminescence data.
Another weakness is that the FD model does not take into account spin splitting, as you mentioned. This can be problematic when studying systems with spin-dependent properties.
The original equation for the energy eigenvalues in the FD model can be found in the original papers by Fock and Darwin, but it can also be found in many textbooks on quantum mechanics or solid state physics.
To learn more about the basic theory of the Fock-Darwin model, I would recommend consulting textbooks or review articles on the subject. You can also find some helpful resources online, such as lecture notes or videos. It may also be helpful to discuss your questions with other researchers in the field.
I hope this helps. Good luck with your research!