In topological insulators the bulk boundary correspondence is frequently stated as the principle that the number of edge modes equals the difference in Chern numbers at that edge. I found this e.g. in "Topological Band Theory and the
Z2 Invariant" by C.L. Kane pp.18 . However in there is no "derivation" to this in the text by C.L. Kane.
Can anyone present to me an argument (maybe even a proof) that the number of edge states corresponds to the change in Chern numbers? A source where I can find such an argument would also be great!
Best Answer
There seems to be no general but simple derivation to this fact. However there are some papers concerning the issue that involve mathematical techniques too advanced for me still. The works that I found are
Bulk-Edge Correspondence for Chern Topological Phases: A Viewpoint from a Generalized Index Theorem. T. Fukui, K. Shiozaki, T. Fujiwara, S. Fujimoto. J. Phys. Soc. Jpn. 81 114602, (2012); arXiv:1206.4410.
Edge states and the bulk-boundary correspondence in Dirac Hamiltonians. Roger S. K. Mong, Vasudha Shivamoggi. Phys. Rev. B 83, 125109 (2011); arXiv link
I also found some lecture notes on the topic also giving some more detailed background information at arXiv:1501.02874. Maybe it helps somebody.