In this talk I will present our recent investigations on
possible topological phases in (111) heterostructures of transition metal
oxide. These (111) heterstructures are promising systems to realize many 2D
topological phases at high temperatures, even with strong correlations, which
is hard to be achieved in conventional materials.
Several examples will be discussed, including high-temperature
quantum spin hall effect in LaAlO3/LaAuO3/LaAlO3 bilayer, correlation induced
topological phases in LaAlO3/LaNiO3/LaAlO3 multilayer, nearly flat topological
band with C=2 (C: Chern number) in SrIrO3 trilayer, and abelian/nonabelian
fractional quantum hall effects in the absence of Landau levels (fractional
Chern insulators). If time is allowed, I will also briefly introduce our work
on classifying wavefunctions of fractional Chern/topological insulators.