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3D Quantum Hall Effect Manipulated by Chiral Landau Levels in Weyl Semimetals

We investigate the 3D quantum Hall effect in Weyl semimetals and elucidate a global picture of the edge states. The edge states hosting 3D quantum Hall effect are combinations of Fermi arcs and chiral bulk Landau levels parallel to the magnetic field. The Hall conductance, $σ_{xz}^H$, shows quantized plateaus at Weyl nodes while tuning the magnetic field. However, the chiral Landau levels manipulate the quantization of Weyl orbits, especially under a tilted magnetic field, and the resulting edge states lead to distinctive Hall transport phenomena. A tilted magnetic field contributes an intrinsic initial value to $σ_{xz}^H$ and such initial value is determined by the tilting angle $θ$. Particularly, even if the perpendicular magnetic field is fixed, $σ_{xz}^H$ will change its sign with an abrupt spatial shift of edge states when $θ$ exceeds a critical angle $θ_c$ in an experiment. Our work uncovers the unique edge-state nature of 3D quantum Hall effect in Weyl semimetals.