  We report the appearance of nontrivial topological phases in a tight-binding
model on the stuffed honeycomb lattice. The model contains nearest neighbor and
next nearest neighbor hopping terms coupled with an additional phase depending
on the direction of hopping. Chern insulating and semi-metallic phases emerge
with the change of hopping parameters. Nonzero Chern numbers characterizing the
bands and the existence of topologically protected edge states in the gap
between the relevant bands confirm the presence of those phases. We show that
adding an extra basis to Haldane's honeycomb model can lead to an additional
topological phase characterized by Chern number $\pm2$. Transition between
different topological phases driven by the hopping parameters has been
illustrated in the topological phase diagram of the system. Zero temperature
Hall conductivity along with density of states is evaluated. Topological
properties of another tight-binding model on the stuffed square lattice are
also reported in this article.
