  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.
