Intervalley magnetism and superconductivity in sign-problem-free models of topological flat bands

Recent experiments in magic angle twisted bilayer graphene have shown a complex phenomenology driven by the interplay between electron correlation and band topology. Inspired by these experiments, we use numerically exact Quantum Monte Carlo calculations to study a topological flat band model involving both spin and valley degrees of freedom in the presence of electron-electron interactions. The model is sign-problem-free at arbitrary filling of the flat bands and for a range of interaction parameters. In the limit with only projected flat-band degrees of freedom, we find a robust insulating state at half-filling of the flat bands, and a competing superconducting phase when doped away from half-filling. Our findings can account for and provide a route to understand various aspects of the rich phenomenology in topologically non-trivial moiré materials.