  Anderson localization is anticipated to play a pivotal role in the
manifestation of the quantum anomalous Hall effect, akin to its role in
conventional quantum Hall effects. The significance of Anderson localization is
particularly pronounced in elucidating the reasons behind the fragility of the
observed quantum anomalous Hall state in the intrinsic magnetic topological
insulator MnBi2Te4 with a large predicted magnetic gap. Here, employing varying
sized MnBi2Te4 micro/nano-structures fabricated from a single
molecular-beam-epitaxy-grown thin film, we have carried out a systematic size-
and temperature-dependent study on the transport properties of the films
regarding the quantum anomalous Hall states. The low-temperature transport
properties of the finite-sized MnBi2Te4 samples can be quantitatively
understood through Anderson localization, which plays an indispensable role in
stabilizing the ground states. At higher temperatures, the failure of electron
localization induced by an excessively short electronic dephasing length is
identified as the cause of deviation from quantization. The work reveals that
electronic dephasing and localization are non-negligible factors in designing
high-temperature quantum anomalous Hall systems.
