The three-dimensional (3D) quantum Hall effect (3DQHE) was initially proposed to be realized in systems with spontaneous charge-density-wave (CDW) or spin-density-wave (SDW), which has stimulated recent experimental progress in this direction. Here,
instead of such intrinsic scenarios, we propose to realize the 3DQHE in a synthetic semiconductor superlattice. The superlattice is engineered along one direction, which is modeled by the Kronig-Penney type periodic potential. By applying a magnetic field along this direction, quantized 3D Hall conductivity can be achieved in certain parameter regimes, along with a vanishing transverse conductivity. We show that such results are robust against the disorder effect and can be hopefully realized by state-of-the-art fabrication techniques. Our work opens a new research avenue for exploring the 3DQHE in electronic superlattice structures.
