  Recently, the field of strongly correlated electrons has begun an intense
search for a correlation induced topological insulating phase. An example is
the quadratic band touching point which arises in a checkerboard lattice at
half-filling, and in the presence of interactions gives rise to topological
Mott insulators. In this work, we perform a mean-field theory computation to
show that such a system shows instability to topological insulating phases even
away from half-filling (chemical potential $\mu = 0 $). The interaction
parameters consist of on-site repulsion ($ U $), nearest-neighbour repulsion ($
V $), and a next-nearest-neighbour correlated hopping ($ t_\text{c} $). The
$t_\text{c}$ interaction originates from strong Coulomb repulsion. By tuning
the values of these parameters, we obtain a desired topological phase that
spans the area around $(V = 0 , \mu = 0)$, extending to regions with
$(V>0,\mu=0)$ and $(V>0,\mu>0)$. This extends the realm of current experimental
efforts to find these topological phases.
