We show that the thin films of Weyl semimetals have a regime of parameters in which they develop very flat Landau bands under strong magnetic fields. Addressing the case of thin films in a perpendicular magnetic field, we observe that two different types of Landau states may arise depending on whether the line connecting a pair of opposite Weyl nodes is parallel or perpendicular to the direction of the magnetic 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 either case, the states in the flat levels are confined along longitudinal sections of the thin film, turning into edge states with distinctive profiles at the lateral boundaries for the two different types of Hall effect.
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