  The exsitance of three-dimensional Hall effect (3DQHE) due to spontaneous
Fermi surface instabilities in strong magnetic field was proposed decades ago,
and has stimulated recent progress in experiments. The reports in recent
experiments show that the Hall plateaus and vanishing transverse
magneto-resistivities (TMRs) (which are two main signatures of 3DQHE) are not
easy to be observed in natural materials. And two main different explanations
of the slow varying slope like Hall plateaus and non-vanishing
  TMRs (which can be called as quasi-quantized Hall effect (QQHE)) have been
proposed. By studying the magneto-transport with a simple effective periodic 3D
system, we show how 3DQHE can be achieved in certain parameter regimes at
first. We find two new mechanisms that may give rise to QQHE. One mechanism is
the "low" Fermi energy effect, and the other is the "strong" impurity effect.
Our studies also proved that the artificial superlattice is an ideal platform
for realizing 3DQHE with high layer barrier periodic potential.
