The Landau level approach to twisted homobilayer transition metal dichalcogenides

Recent experiments on twisted MoTe₂ have reported the first observation of the fractional quantum anomalous Hall effect (FQAHE), demonstrating exotic gapped states with broken time-reversal symmetry and fractionally charged excitations. Low-energy continuum model descriptions of transition metal dichalcogenide (TMD) twisted homobilayers that have $K$-valley valence band maxima, such as MoTe₂ and WSe₂, indicate that their topmost moiré minibands carry non-zero Chern numbers and become almost flat at a magic angle. Additional studies showed that the quantum geometry of the band is nearly ideal at the magic angle, suggesting a connection to the physics of the lowest Landau level that is responsible for the FQAHE stabilization. In this talk, I will introduce an approximation to the continuum model that explicitly maps the system to an effective problem of Landau levels in a periodic potential. Our model explains why magic angles emerge and why the quantum geometry is almost ideal. I will discuss the regime of validity of the approach and how it is a powerful starting point for the study of interactions, promising to shed light on some of the questions raised by the experiments.