  In the present paper, the Gutzwiller density functional theory (LDA+G) has
been applied to study a bilayer system of LaCoO$_3$ grown along the $(111)$
direction on SrTiO$_3$. The LDA calculations show that there are two nearly
flat bands located at the top and bottom of $e_{g}$ bands of Co atoms with the
Fermi level crossing the lower one, which is almost half-filled. After
including both the spin-orbit coupling and the Coulomb interaction in the LDA+G
method, we find that the interplay between spin-orbit coupling and Coulomb
interaction stabilizes a very robust ferromagnetic insulator phase with
non-zero Chern number, which indicates the possibility to realize quantum
anomalous Hall effect in this system.
