Itinerant electron ferromagnetism in moiré materials

Moiré materials are artificial two-dimensional crystals with flexibly tunable properties. I will survey some possibilities for realizing flexible itinerant electron ferromagnetism in moiré materials, including single-band Nagaoka-like ferromagnetism, and multi-band ferromagnetism that is analogous to that of transition metal ferromagnets. Our analysis of moiré ferromagnetism is dependent on derivations of effective models that describe the electronic physics accurately at the moiré scale, and on numerical many-body methods used to analyze competitions between different types of electronic order. Emphasis will be placed on using finite-temperature Lanczos methods to estimate the highest possible Curie temperatures that are likely to be achievable in graphene multilayers, transition metal dichalcogenide multilayers, and in other two-dimensional material stacks containing moirés.