This discussion focuses on recommended introductory resources for studying Topological Superconductors, specifically the Kitaev model. Key resources include the review by Hasan and Kane on topological insulators (arXiv:1002.3895), a theoretical introduction (arXiv:1608.03395), and Kitaev's original paper on the 1D spinless fermion chain (arXiv:cond-mat/0010440). Participants emphasize the importance of a solid understanding of second quantization and suggest practical projects involving Hamiltonians, Fourier transforms, and numerical solutions using MATLAB.
PREREQUISITESResearchers, graduate students, and physicists interested in condensed matter physics, particularly those focusing on topological superconductors and quantum mechanics.
Thank you a lot. In fact my Goal is to understand Kitaev model. But i am afraid if i should have some basics before start reading. I know Quantum Mechanics, second quantization... But i am wondering if i need further things.DeathbyGreen said:A great place to start is a review by Hasan and Kane on topological insulators:
https://arxiv.org/pdf/1002.3895.pdf
A more theory based introduction can be found here:
https://arxiv.org/pdf/1608.03395.pdf
If you're looking for interesting introductions, the 1D spinless fermion chain with p-wave superconductivity by Kitaev is a good model to see the dynamics. A good professor to look at did some notes here:
https://arxiv.org/pdf/1206.1736.pdf
And you can look at all the references those papers cite to continue down the rabbit hole.
shiraz said:Thank you a lot. In fact my Goal is to understand Kitaev model. But i am afraid if i should have some basics before start reading. I know Quantum Mechanics, second quantization... But i am wondering if i need further things.
Thank you a lot for your help
Really Thank you. I will do that sure. Good luck in your researchDeathbyGreen said:No problem! As long as you have a background with some second quantization you should be fine. If you really want to understand the kitaev model, I would start with the original paper:
https://arxiv.org/abs/cond-mat/0010440
Then, maybe work through a little project:
1. start with the real space Hamiltonian and Fourier transform into momentum space, using periodic boundary conditions in x and y; perform a Bogoliubov transformation and diagonalize to get an expression for the dispersion relation. Then try to find:
- The spectrum E(k)
- The density of states D(E)
- The wavefunctions (eigenvectors)
3. Now make the chain finite (use the real space model) and solve numerically (simple MATLAB eig(H) type function will do the trick). You should find
- The spectrum E(k)
- The density of states D(E)
- The wavefunctions
4. Reflect on the comparison between the two cases.
5. Also take a look at the review
https://arxiv.org/pdf/1202.1293.pdf
and use it's suggestions to calculate the Chern number, which will give you some insight into topology. The best way to learn this stuff is to really push through the math!