Relations between chern number and edge state

[taishizhiqiu]

I have been doing a literature survey about topological insulators for some time. What surprises me is the close relation between difference of chern number and number of edge states. However, I found most review or tutorial in topological insulator avoided direct proof of the relation. So can someone tell me where the rigorous proof of the relation can be found?

 

[BigJDubs]

Any help would be greatly appreciated!The relation between the difference of Chern numbers and the number of edge states can be found in a paper by H. Watanabe and S. Murakami, “Edge states and the bulk-edge correspondence for two-dimensional topological insulators”. The paper provides a rigorous proof of the relation, as well as an explanation of its implications. The paper can be accessed here: https://arxiv.org/pdf/1202.1771.pdf