Surface and bulk Landau levels in thin films of Weyl semimetals

We show that the thin films of Weyl semimetals have a regime in which they develop an ordered sequence of Landau bands where the holelike levels are disentangled from their electronlike counterparts. We stress that this is not, however, a generic situation since in some cases there may be an inversion of Landau bands with electron- and holelike character, preventing a clean observation of conductance quantization. Furthermore, we observe that two different types of Landau states may arise in thin films under perpendicular magnetic field, depending on whether the line connecting a pair of opposite Weyl nodes is parallel or perpendicular to the direction of the field. In the latter instance, we show that the flat Landau bands are made of states peaked at the two faces of the thin film. When the line connecting the Weyl nodes is parallel to the magnetic field, we see instead that the states in the Landau bands take the form of stationary waves with significant amplitude across the bulk of the material. In the regime with the ordered sequence of Landau bands, the states in the flat domains are confined along longitudinal sections of the thin film, and they start to disperse as long as the longitudinal propagation becomes close to the edges of the film, leading to edge states with distinctive profiles at the lateral boundaries for the two different types of Hall effect.