Theoretical study for 3D quantum Hall effect in a periodic electron system

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.