Solid State Which Introductory Books Are Best for Studying Topological Superconductors?

[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.

 

[DeathbyGreen]

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]

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

 

[DeathbyGreen]

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!

 

[shiraz]

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