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 Landau bands dispersing along the magnetic field direction. The Hall conductance, ${\sigma }_{xz}^H$ [see Fig. 4], shows quantized plateaus with the variance of the magnetic field when the Fermi level is at the Weyl node. However, the chiral Landau bands can change the spatial distribution of the edge states, especially under a tilted magnetic field, and the resulting edge states lead to distinctive Hall transport phenomena. A tilted magnetic field contributes an intrinsic value to ${\sigma }_{xz}^H$ and such an intrinsic value is determined by the tilting angle $\theta$ between the magnetic field and the $y$ axis [see Fig. 1(c)]. Particularly, even if the perpendicular magnetic field is fixed, ${\sigma }_{xz}^H$ will change its sign with an abrupt spatial shift of the edge states when $\theta$ exceeds a critical angle ${\theta }_c$. Our work uncovers the novel edge-state nature of the 3D quantum Hall effect in Weyl semimetals.

• Received 28 February 2020
• Revised 8 May 2020
• Accepted 2 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.036602