  Chiral edge modes inherent to the topological quantum anomalous Hall (QAH)
effect are a pivotal topic of contemporary condensed matter research aiming at
future quantum technology and application in spintronics. A large topological
gap is vital to protecting against thermal fluctuations and thus enabling a
higher operating temperature. From first-principle calculations, we propose
Al$_{2}$O$_{3}$ as an ideal substrate for atomic monolayers consisting of Bi
and group-III elements, in which a large-gap quantum spin Hall effect can be
realized. Additional half-passivation with nitrogen then suggests a topological
phase transition to a large-gap QAH insulator. By effective tight-binding
modelling, we demonstrate that Bi-III monolayer/Al$_{2}$O$_{3}$ is dominated by
$p_{x}, p_{y}$ orbitals, with subdominant $p_z$ orbital contributions. The
topological phase transition into the QAH is induced by Zeeman splitting, where
the off-diagonal spin exchange does not play a significant role. The effective
model analysis promises utility far beyond Bi-III monolayer/Al$_{2}$O$_{3}$, as
it should generically apply to systems dominated by $p_{x}, p_{y}$ orbitals
with a band inversion at $\Gamma$.
