  The quantum Hall effect (QHE) is a topologically protected phenomenon which
has been observed in various systems. In experiments, the size of Hall bar
device to realize the QHE is generally much larger than the phase coherence
length, in which the quantum coherence of electrons is destroyed. Here, we
theoretically study the influence of dephasing effect on the quantized Hall
(QH) plateaus. We find that the QH plateau disappears in perfectly quantum
coherent systems if the coupling between leads and central region is imperfect.
The Hall resistance is very large and strongly oscillates instead of presenting
the QH plateau in this case. However, by introducing the dephasing, the Hall
resistance decreases and the QH plateau appears gradually. Similar results can
also be observed for the quantum anomalous Hall effect. Our results propose
that dephasing effect promotes the appearance of QH plateaus, which opens a new
topic of the dephasing effect on topological systems.
