Landau Level Description of Topological Bands in Twisted Homobilayer TMDs

Topological flat bands and nearly ideal quantum geometry have been identified in twisted homobilayer transition metal dichalcogenide (TMD) moiré superlattices, and are thought to be crucial for understanding the recently observed fractional Chern insulating state in twisted MoTe2. Recent theoretical work proposes an adiabatic approximation which maps the bilayer valence bands to a system of charged particles in a nonuniform magnetic field and a periodic potential. Here, we study the non-interacting band structure using a basis constructed from Landau levels (LLs) formed by the spatially averaged part of the effective magnetic field. We find that Landau-level mixing can have a strong effect on the band properties, whereas higher harmonics of the periodic field and potential have a weaker effect. Upon including several LLs, the nonuniformity of Berry curvature, the nearly ideal quantum geometry at the magic angle and the value of the magic angle are qualitatively reproduced by the adiabatic approximation, which works better for WSe2 than MoTe2.