  We study the practicability of achieving quantum anomalous Hall (QAH) effect
with field-tunable Chern number in a magnetically doped, topologically trivial
insulating thin film. Specifically in a candidate material,
TlBi(S$_{1-\delta}$Se$_{\delta}$)$_2$, we demonstrate that the QAH phases with
different Chern numbers can be achieved by means of tuning the exchange field
strength or the sample thickness near the Z2 topological critical point. Our
physics scenario successfully reduces the necessary exchange coupling strength
for a targeted Chern number. This QAH mechanism differs from the traditional
QAH picture with a magnetic topological insulating thin film, where the
"surface" states must involve and sometimes complicate the realization issue.
Furthermore, we find that a given Chern number can also be tuned by a
perpendicular electric field, which naturally occurs when a substrate is
present.

Mesoscale and Nanoscale Physics