Theoretical study of the three-dimensional quantum Hall effect in a periodic electron system

The existence of a three-dimensional quantum Hall effect (3D QHE) due to spontaneous Fermi surface instabilities in strong magnetic fields was proposed decades ago, and has stimulated recent progress in experiments. The reports in recent experiments show that the Hall plateaus and vanishing transverse magnetoresistivities (TMRs) (which are two main signatures of 3D QHE) are not easily observed in natural materials. Two main explanations for the slowly varying slopelike Hall plateaus and nonvanishing TMRs [which can be referred to as the quasiquantized Hall effect (QQHE)] have been proposed. By studying the magnetotransport with a simple effective periodic 3D system, we show how 3D QHE can be achieved in certain parameter regimes. We find two 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 prove that an artificial superlattice is an ideal platform for realizing 3D QHE with a high layer barrier periodic potential.