  Topological phases have attracted much interest in recent years. While there
are a number of three-dimensional materials exhibiting topological properties,
there are relatively few two-dimensional examples aside from the well-known
quantum Hall systems. Here we make materials-specific predictions for
topological phases using density functional theory combined with Hartree-Fock
theory that includes the full orbital structure of the relevant iridum
$d$-orbitals and the strong but finite spin-orbit coupling strength. We find
Y$_2$Ir$_2$O$_7$ bilayer and trilayer films grown along the [111] direction can
support topological metallic phases with a direct gap of up to 0.02 eV, which
could potentially bring transition metal oxides to the fore as a new class of
topological materials with potential applications in oxide electronics.
