Abstract: Moiré materials have been established as a new paradigm for realizing exotic phases of matter, attracting prominent attention due to their unprecedented tunability. Notably, moiré materials based on transition metal dichalcogenides (TMDs) provide a robust platform to investigate quantum phases that emerge in both topologically trivial and non-trivial flat bands. In this talk I will review theoretical studies of the many-body physics of semiconductor moiré materials that I have performed during my PhD. Our work sheds light on the microscopic mechanisms underlying the diverse quantum phases observed in moiré TMDs, such as Mott insulators, generalized Wigner crystals, and fractional Chern insulators. 

In the first part of the talk, I will describe how the extended nature of Wannier functions for moiré Hubbard simulators makes nonlocal interactions relevant, favoring phases such as Mott ferromagnets and quantum spin liquids. In the second part of the talk, I will introduce an approximation to the continuum model for homobilayer TMDs, which maps the system to an effective problem of Landau levels in a periodic potential. This approach explains the origin of a magic angle with almost vanishing band width and nearly ideal quantum geometry in topological moiré TMDs. I will conclude by discussing the numerous possibilities that the field of semiconductor moiré materials provides for discovering new phases of matter.