Bulk-edge correspondence for Chern topological phases: A viewpoint from   a generalized index theorem
  We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear dispersion but also with higher order derivatives arising from generic band structures. Using a generalized index theorem valid for such systems, we show the equivalence between the spectral flow of the edge states and the Chern numbers specifying the bulk systems. 
T. Fukui, K. Shiozaki, T. Fujiwara, and S. Fujimoto
cond-mat.mes-hall