Best resources to learn topological condensed matter in 2022?

[Amentia]

Hello,

I was not sure whether this should belong to this section or the condensed matter section. I am wondering if after about 15 years in research in topological condensed matter, there exist well-recognized references for beginners in the topic. Books or courses but also review articles, videos, online courses, any format.

I call a beginner someone who knows nothing about topology but will make any necessary effort to understand the mathematics needed to get into the topic. So the mathematical level needed to understand the resources does not matter, but how comprehensive and well-explained the field of research is, that is what matters!

Thank you in advance for your suggestions.

 

[malawi_glenn]

Altland and Simmons book contains a chapter of it, you can start from there.

 

[Demystifier]

For a really basic introduction, I like the Nobel 2016 review.
https://www.nobelprize.org/uploads/2018/06/advanced-physicsprize2016-1.pdf

 

[Amentia]

Thank you both for your answers. I already have the book by Altland and Simmons called Condensed Matter Field Theory, so I assume it is the one you refer to. I only need to find the chapter now! And the Nobel review looks great to start learning about the topic.

For interested people I have also found this online course which is recent, so I don't know how good it is, but I will give it a try:
https://www.edx.org/course/topological-states-of-matter

And also an older one at this address:
https://topocondmat.org/

 

[malawi_glenn]

I only need to find the chapter now!

in 2nd edition its chapter 9.

 

[martinbn]

I bit off topic, but I have to say that I find all these topological applications very disappointing. It may be simply because I haven't seen enough, but everything that I have looked at has very little topology in it. I would like to see some applications where the topology needed is more than what Maxwell knew (implicitely) about topology, after all topolygy has been developed a lot since the mid 19th century.

 

[Demystifier]

It may be simply because I haven't seen enough

Yes, you haven't seen enough. There are many papers, for instance, using K-theory in condensed matter physics, see e.g.
https://arxiv.org/abs/hep-th/0503006
https://sites.google.com/view/dmonaco/teaching/k-theory-in-condensed-matter-physics

 

[martinbn]

Yes, you haven't seen enough. There are many papers, for instance, using K-theory in condensed matter physics, see e.g.
https://arxiv.org/abs/hep-th/0503006
https://sites.google.com/view/dmonaco/teaching/k-theory-in-condensed-matter-physics

Do you have anything else? The paper doesn't have much of anything, the lecture notes seem to have only mathematical definitions and constructions but no physics nor applications to physics!