Interaction-driven phases at various fillings of the quasiflat band in a moiré ladder.

Motivated by moiré graphene, we study its one-dimensional counterpart: a moiré ladder. Our model comprises a two-leg fermionic ladder, threaded by a flux and a spatially varying interleg hopping term. In a recent study, it has been shown that such a model hosts a quasiflat low-energy band, with unusual ground state at half filling in the presence of interaction -- a ferromagnetic Mott insulator. In this talk we show that while the metal-insulator transition can be understood within a perturbative picture, the ferromagnetic spin-spin correlation is a truly nonperturbative aspect. We extend the study of the latter to other fillings of the quasiflat band--one-quarter, three-quarters, slightly above half filling (half filling plus two electrons), and slightly below half-filling (half filling minus two electrons)--using the Density Matrix Renormalization Group method. We find that the spin-spin correlation is ferromagnetic at fillings less than half, similar to that observed at half filling, but is antiferromagnetic beyond half filling. Interestingly, these results hold only when mixing between the lowest quasiflat band and the next-to-lowest dispersive band is negligible; once mixing between the two bands is facilitated by increasing the interaction strength, the correlation becomes ferromagnetic above half filling as well. Additionally, by reducing the strength of the interaction in comparison to the bandwidth, a transition from the ferromagnetic to the antiferromagnetic state is observed in all the cases.