Who proposed the bulk-edge correspondence principle? Who proposed the bulk-edge correspondence principle?
The principle is often quoted in counting the number of zero energy states localized on the interface between two insulators with distinct band topology. However, I could not retrieve who was the first to say that.
 A: I believe it was Xiao-Gang Wen in 1989, see also this 1994 paper by him and his collaborators

http://dao.mit.edu/~wen/pub/ednab.pdf

He's at MIT. I was once hosting a seminar by him, he is one of the most creative and playful folks in this segment of condensed matter physics. The paper above contains some other relevant references, including a paper by Wen and Tony Zee.
A: Maybe it is R. Jackiw and C. Rebbi (Phys. Rev. D 13, 3398)
When explaining the quantum Hall effect, Hasan and Kane (Rev. Mod.Phys. 2010, 82: 3045–3067) said "This interplay between topology and gapless modes is ubiquitous in physics and has appeared in many contexts. It was originally found by Jackiw and Rebbi (1976) in their analysis of a 1D field theory" in pages 3048-3049.
A: @Hai-Yao Deng. I hope that by now you might have found the answer to your question. I have recently started reading about the topological phases of matter. I find that in his paper, Y. Hatugai PRB 48, 1993 study in detail about this correspondence for the integer quantum Hall effect. He also summaries a sort of development of the argument from TKNN calculation of Hall conductance to the numerical computation of edge states in the same system by Rammal, Toulouse, Jaekel, and Halperin. 
