Magic Angles and Fractional Chern Insulators in Twisted Homobilayer Transition Metal Dichalcogenides.

We explain the appearance of magic angles 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 provides a simple qualitative explanation for the nearly ideal quantum geometry of the lowest moiré miniband at particular twist angles, predicts that topological flat bands occur only when the valley-dependent moiré potential is sufficiently strong compared to the interlayer tunneling amplitude, and provides a convenient starting point for the study of interactions.

Nonlocal Interactions in Moiré Hubbard Systems.

Moiré materials formed in two-dimensional semiconductor heterobilayers are quantum simulators of Hubbard-like physics with unprecedented electron density and interaction strength tunability. Compared to atomic scale Hubbard-like systems, electrons or holes in moiré materials are less strongly attracted to their effective lattice sites because these are defined by finite-depth potential extrema. As a consequence, nonlocal interaction terms like interaction-assisted hopping and intersite exchange are more relevant. We theoretically demonstrate the possibility of tuning the strength of these coupling constants to favor unusual states of matter, including spin liquids, insulating ferromagnets, and superconductors.