Recently, the Hofstadter spectrum of a twisted ${\mathrm{WSe}}_2/{\mathrm{MoSe}}_2$ heterobilayer was observed in experiment [C. R. Kometter et al. Nat. Phys. 19, 1861 (2023)], but the origin of Hofstadter states remains unclear. Here, we present a comprehensive theoretical interpretation of the observed Hofstadter states by calculating their accurate Hofstadter spectrum. We point out that the valley Zeeman effect, a unique feature of the transition metal dichalcogenide (TMD) materials, plays a crucial role in determining the shape of the Hofstadter spectrum, due to the narrow bandwidth of the moiré bands. This is distinct from the graphene-based moiré systems. We further predict that the Hofstadter spectrum of the moiré flat band, which was not observed in the experiment, can be observed in the same system with a larger twist angle $2^{\circ }\lesssim \theta \lesssim 3^{\circ }$. Our theory paves the way for further studies of the interplay between the Hofstadter states and correlated insulating states in such moiré lattice systems.

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• Landau levels
• Quantum Hall effect
• Twistronics
• Bilayer films
• Transition metal dichalcogenides