Magic Angles and Fractional Chern Insulators in Twisted Homobilayer TMDs

We explain the appearance of magic angle flat bands and fractional Chern insulators in twisted K-valley homobilayer transition metal dichalcogenides by mapping their continuum model to a Landau level problem. Our approach relies on an adiabatic approximation for the quantum mechanics of valence band holes in a layer-pseudospin field that is valid for sufficiently small twist angles and on a lowest Landau level approximation that is valid for sufficiently large twist angles. It simply explains why the quantum geometry of the lowest moir\'e miniband is close to ideal at the flat-band twist angle, predicts that flat bands occur only when the valley-dependent moir\'e potential is sufficiently strong compared to the interlayer tunneling amplitude, and provides a powerful starting point for the study of interactions.