  In this paper, we study a one-dimensional boson system in a superlattice
potential.This system is experimentally feasible by using ultracold atomic
gases,and attracts much attention these days. It is expected that the system
has a topological phase called topological Mott insulator (TMI). We show that
in strongly-interacting cases, the competition between the superlattice
potential and the on-site interaction leads to various TMIs with non-vanishing
integer Chern number. Compared to hard-core case, the soft-core boson system
exhibits rich phase diagrams including various non-trivial TMIs. By using the
exact diagonalization,we obtain detailed bulk-global phase diagrams including
the TMIs with high Chern numbers and also various non-topological phases. We
also show that in adiabatic experimental setups, the strongly-interacting
bosonic TMIs exhibit the topological particle transfer, i.e., topological
charge pumping phenomenon, similarly to weakly-interacting systems. The various
TMIs are characterized by topological charge pumping as it is closely related
to the Chern number, and therefor the Chern number is to be observed in
feasible experiments.
