Studying How start studying Topological Insulators

[trustinlust]

Hi all,

I'am starting a Phd In Theoretical Condensed Matter Physics, and I would like to produce a thesis on the Topological Insulators topic. Unfortunately I don't have a background in Consensed Matter Physics (in my curriculum there are exams about General Relativity, Quantum Field Theory and Statistical Mechanics) and I know only a bit of Solid State Physics. So, here's the question: what are the initial and essential topics which I should study and know (and on which books) to start managing (in a good way) topological insulators as soon as possible?

Thanks

 

[xepma]

This article should be your starting point:
http://arxiv.org/abs/1002.3895

Not only does it provide a very nice introduction into the field, it also provides a large number of references to articles which started the field.

It's hard to point out what you exactly need to know to understand these papers. Part of a PhD is to figure out what mathematical tools and physical principles you need to learn to understand the articles and perform your own research. If you have had a solid introduction into Quantum Field Theory then I highly recommend diving into one or more books on quantum field theory methods in condensed matter physics, such as:

https://www.amazon.com/dp/0521769752/?tag=pfamazon01-20
https://www.amazon.com/dp/0198566336/?tag=pfamazon01-20

These books are should be accessible enough.

A very important aspect of topological insulators that comes to mind is electron band theory. A book on solid state physics like Ashcroft and Mermin or Kittel should do the trick.

Another mathematical tool that is frequently used is that of Chern classes. Try Nakahara.

But again, start with the article I mentioned in the beginning (Kane is one of the people that made this field what it is today). Dig up the articles they refer to -- you'll soon come across concepts that you won't be familiar with. The trick is to find a proper source which explains it.

 

[trustinlust]

Thanks for the exhaustive reply, Xepma. Only some other question.

Do you refer to "Geometry, Topology and Physics" Nakahara's book? Is it correct?

Someone told me that Quantum Hall Effect is the starting point of all the topological problems in Condensed Matter, and that it should be useful to start studying this subject. Can you give me some references for this topic too?

Thanks

 

[trustinlust]

An other question:

In future I would like studying Strongly Correlated Systems in Condensed Matter, too. Do you think these two topics (Strongly Correlated Systems and Topological Insulators) are correlated? Or it would be - considering how highly specialized the research in physics is, nowadays - a considerable change of research area? (different methods, different mathematical tools used,...)

 

[Monocles]

I studied the quantum hall effect in the spring as a reading course, and I mostly read the original papers. As long as you have some basic knowledge of solid-state physics, they are pretty accessible as long as you start at the beginning and then work your way up. I found the original papers more useful than textbooks since they went into much more detail. Eventually you'll need to learn some algebraic topology to get the full picture (that's where Chern classes come up, as mentioned above).