# 3D quantum Hall effect of Fermi arcs in topological semimetals

## TL;DR

This paper predicts a novel 3D quantum Hall effect in topological semimetals arising from Fermi arcs, enabled by Weyl node tunneling, with unique edge states and quantized Hall plateaus observable via gating.

## Contribution

It introduces a mechanism for 3D quantum Hall effect in topological semimetals through Fermi arc tunneling, distinct from surface states in topological insulators.

## Key findings

- Fermi arcs can form complete loops via Weyl node tunneling.
- Hall conductivity shows transition from 1/B dependence to quantized plateaus.
- The effect can be realized in materials like TaAs, Cd3As2, Na3Bi.

## Abstract

The quantum Hall effect 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, giving an example of (d-2)-dimensional boundary states. 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 sheet Hall conductivity 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.