  It is known that the Atiyah-Patodi-Singer index can be reformulated as the
eta invariant of the Dirac operators with a domain wall mass which plays a key
role in the anomaly inflow of the topological insulator with boundary. In this
paper, we give a conjecture that the reformulated version of the
Atiyah-Patodi-Singer index can be given simply from the Berry phase associated
with domain wall Dirac operators when adiabatic approximation is valid. We
explicitly confirm this conjecture for a special case in two dimensions where
analytic calculation is possible. The Berry phase is divided into the bulk and
the boundary contributions, each of which gives the bulk integration of the
Chern character and the eta-invariant.
