Three-dimensional quantum Hall effect in the excitonic phase of a Weyl semimetal

The quantum Hall effect (QHE) is usually observed in two-dimensional systems. Recently, the QHE has been proposed to exist in three-dimensional (3D) Weyl semimetals when the Fermi energy is precisely at the Weyl nodes at zero temperature, which is hardly achievable experimentally. However, the QHE has been experimentally realized in the 3D topological semimetal ${\text{Cd}}_{3}{\text{As}}_{2}$ at finite temperatures. It has been found that a Weyl semimetal may translate to a chiral excitonic insulator due to the interplay between the interaction and band topology. In a Weyl semimetal slab, we show that the Fermi arc surface states can exist not only in the Weyl semimetal but also in the chiral excitonic insulator. As long as the Fermi energy crosses the Fermi arc states, the QHE can be generated under the combined action of bulk states and Fermi arc surface states. Therefore, the integer quantization of Hall conductivity can be observed for a finite energy range, or equivalently at finite temperatures.