Possible interaction driven topological phases in (111) bilayers of LaNiO$_3$

We use the variational mean-field approach to systematically study the phase diagram of a bilayer heterostructure of the correlated transition metal oxide LaNiO$_3$, grown along the (111) direction. The Ni$^{3+}$ ions with $d^7$ (or $e_g^1$) configuration form a buckled honeycomb lattice. We show that as a function of the strength of the on-site interactions, various topological phases emerge. In the presence of a reasonable size of the Hund's coupling, as the correlation is tuned from intermediate to strong, the following sequence of phases is found: (1) a Dirac half-semimetal phase, (2) a quantum anomalous Hall insulator (QAHI) phase with Chern number one, and (3) a ferromagnetic nematic phase breaking the lattice point group symmetry. The spin-orbit couplings and magnetism are both dynamically generated in the QAHI phase.