The quantum Hall effect is usually observed in 2D systems. We show that theFermi arcs can give rise to a distinctive 3D quantum Hall effect in topologicalsemimetals. Because of the topological constraint, the Fermi arc at a singlesurface has an open Fermi surface, which cannot host the quantum Hall effect.Via a "wormhole" tunneling assisted by the Weyl nodes, the Fermi arcs atopposite surfaces can form a complete Fermi loop and support the quantum Halleffect. The edge states of the Fermi arcs show a unique 3D distribution, givingan example of (d-2)-dimensional boundary states. This is distinctly differentfrom the surface-state quantum Hall effect from a single surface of topologicalinsulator. As the Fermi energy sweeps through the Weyl nodes, the sheet Hallconductivity evolves from the 1/B dependence to quantized plateaus at the Weylnodes. This behavior can be realized by tuning gate voltages in a slab oftopological semimetal, such as the TaAs family, Cd$_3$As$_2$, or Na$_3$Bi. Thiswork will be instructive not only for searching transport signatures of theFermi arcs but also for exploring novel electron gases in other topologicalphases of matter.
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