Topological Superconductors -- Looking for introductory textbooks or study materials

In summary, If you are interested in studying Topological superconductors, a great place to start is with a review by Hasan and Kane on topological insulators. Another good resource is a theory based introduction found in an article by Hasan and Kane. For more interesting introductions, you can look into the 1D spinless fermion chain with p-wave superconductivity by Kitaev, and check out the notes by a professor on this topic. To further your understanding, you can also look at the references cited in these papers. It is recommended to have a background in Quantum Mechanics and second quantization before diving into the Kitaev model. The best way to learn is by working through the math and experimenting with different calculations.
  • #1
shiraz
Dear All
I am trying to study Topological superconductors but i have no idea about it. Can anyone suggest me an introductory book to start with.
 
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  • #2
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.
 
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Likes Demystifier, shiraz and atyy
  • #3
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.
Thank you alot. 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
 
  • #4
shiraz said:
Thank you alot. 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

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!
 
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Likes shiraz
  • #5
DeathbyGreen 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!
Really Thank you. I will do that sure. Good luck in your research
 

Related to Topological Superconductors -- Looking for introductory textbooks or study materials

1. What is a topological superconductor?

A topological superconductor is a type of material that exhibits both superconducting and topological properties. This means that it can conduct electricity without resistance and also have unique surface properties that are protected from external disturbances.

2. How are topological superconductors different from traditional superconductors?

Traditional superconductors are characterized by the formation of Cooper pairs, which are two electrons bound together to carry electrical current without resistance. In topological superconductors, these Cooper pairs also have a topological property called non-Abelian statistics, which could potentially be used for quantum computing.

3. What are some potential applications of topological superconductors?

Topological superconductors have potential applications in quantum computing, as mentioned before, as well as in creating qubits for quantum information storage and processing. They could also be used in creating more efficient power transmission lines and high-speed electronic devices.

4. What are some key features to look for in an introductory textbook on topological superconductors?

An introductory textbook on topological superconductors should cover the basics of superconductivity and topology, as well as their intersection. It should also include information on current research and potential applications. Visual aids, such as diagrams and illustrations, can also be helpful in understanding the concepts.

5. Are there any recommended study materials or online resources for learning about topological superconductors?

Yes, there are several online resources available for learning about topological superconductors, including lecture notes and videos from universities, scientific articles, and online courses. Some recommended textbooks include "Topological Insulators and Topological Superconductors" by B. Andrei Bernevig and "Topological Superconductivity" by B. Andrei Bernevig and Taylor Hughes.

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