Fractional Chern insulators and composite Fermi liquids vs. charge order in twisted MoTe 2

The bandstructure of twisted MoTe 2 around 3.7 consists of spin-valley locked Chern bands with a bandwidth that is smaller than the interaction scale. As such, the strongly correlated phases familiar from Landau levels can be realized: Quantum Hall states, composite Fermi liquids and charge order. These states have in common that they are all favoured by strong interactions, however changing the quantum geometry and topology of the bands as well as their bandwidth via the displacement field and twist angle tilts the balance between them. We provide a comprehensive exact diagonalization analysis of the competition between these states and in particular elucidate the nature of the charge order at fillings ν=- 14,- 13,- 12,- 23. Furthermore, we analyze the effect of band mixing by going beyond a single band per valley. This effect of band mixing is crucial for reconciling the numerical phase diagrams with experimental observations.