  Correlated electron systems on a honeycomb lattice have emerged as a fertile
playground to explore exotic electronic phenomena. Theoretical and experimental
work has appeared to realize novel behavior, including quantum Hall effects and
valleytronics, mainly focusing on van der Waals compounds, such as graphene,
chalcogenides, and halides. In this article, we review our theoretical study on
perovskite transition-metal oxides (TMOs) as an alternative system to realize
such exotic phenomena. We demonstrate that novel quantum Hall effects and
related phenomena associated with the honeycomb structure could be artificially
designed by such TMOs by growing their heterostructures along the [111]
crystallographic axis. One of the important predictions is that such TMO
heterostructures could support two-dimensional topological insulating states.
The strong correlation effects inherent to TM $d$ electrons further enrich the
behavior.
