  Fractional Chern insulators (FCIs), having properties similar to those of the
fractional quantum Hall effect, have been established numerically in various
toy models. To fully explore their fundamental physics and to develop practical
applications, material realization is indispensable. Here we theoretically
predict a realization of FCI in a two-dimensional organometallic material,
which is known to have the prerequisite topological at bands. Using numerical
exact diagonalization we demonstrate that the presence of strong electronic
correlations and fractional filling of such a system could lead to a rich phase
diagram, including Abelian fractional quantum Hall (FQH), Fermi-liquid, and
Wigner crystal states. In particular, the FQH state has been confirmed
systematically by calculating the topological ground-state degeneracies,
topological Chern number, and the quasihole excitation spectrum as well as the
particle entanglement spectrum. Future experimental realization of the FQH
state in such material may provide a route for developing practical
applications of FCI with no need of the extreme conditions.
