Many body ground states in Moiré flat bands beyond lowest Landau levels

The concept of higher-vortexable bands was developed recently to describe bands that are similar to higher Landau levels rather than lowest Landau levels. Higher Landau levels host fascinating physics beyond the lowest Landau level, such as non-Abelian topological states. We present a new model capable of realizing both the lowest and first Landau levels without an applied magnetic field, and investigate many-body ground states of this model. We find evidence of intriguing many-body interacting ground states at various fillings such as fractional Chern states and Moore-Read states. We also comment on the influence of quantum geometry on the stability of these ground states.