  The topological property of boson-fermion mixture in a one-dimensional
optical superlattice is studied and the topological insulating phase of
interacting boson-fermion mixture characterized by a nontrivial Berry phase is
identified. The single-particle and boson-fermion exchanging excitation
spectrums are calculated and we identify the boson-fermion exchanging
excitation as the gapless topological excitation in the topological phase of
the mixture. The different kinds of excitations are explained explicitly from
the competition among the bulk gap, the on-site boson-boson and boson-fermion
interactions. The Hamiltonian studied has been partly realized in the
state-of-art cold atom experiments, and the results are very relevant to the
experiments.
