3D quantum Hall effect of Fermi arcs in topological semimetals

C. M. Wang, Hai-Peng Sun, Hai-Zhou Lu, X. C. Xie

Published 2017-05-21Version 1

The quantum Hall effect with quantized Hall conductance is usually observed in 2D systems. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs at opposite surfaces can form a complete Fermi loop and support the quantum Hall effect. The edge states of the Fermi arcs show a unique 3D distribution. This is distinctly different from the surface-state quantum Hall effect from a single surface of topological insulator. As the Fermi energy sweeps through the Weyl nodes, the Hall conductance evolves from the $1/B$ dependence to quantized plateaus at the Weyl nodes. This behavior can be realized by tuning gate voltages in a slab of topological semimetal, such as the TaAs family, Cd$_3$As$_2$, or Na$_3$Bi. This work will be instructive not only for searching transport signatures of the Fermi arcs but also for exploring novel electron gases in other topological phases of matter.