3D Quantum Hall Effect

So far, the quantum Hall effect is observed only in 2D systems. We show that the Fermi arcs can give rise to a distinctive quantum Hall effect in topological semimetals in three dimensions [1]. Topological semimetals are 3D topological states of matter, in which the energy bands touch at a finite number of Weyl nodes. They host topologically-protected surface states, known as the Fermi arcs. Via a “wormhole” tunnelling assisted by the Weyl nodes, the Fermi arcs at two opposite surfaces can form a single 2D electron gas and support a quantum Hall effect in three dimensions. Possible signatures of the 3D quantum Hall effect have been observed in several experiments on the topological Dirac semimetal Cd3As2. Our discovery of this 3D quantum Hall give an example of (d-2)-dimensional boundary states, a promising direction in topological states of quantum matter.