Moire versus Mott: Incommensuration and Interaction in One-Dimensional Bichromatic Lattices

Inspired by the rich physics of twisted 2D bilayer moire systems, we study Coulomb interacting systems subjected to two overlapping finite ID lattice potentials of unequal periods through exact numerical diagonalization. Unmatching underlying lattice periods lead to a 1D bichromatic moire superlattice with a large unit cell and consequently a strongly flattened band, exponentially enhancing the effective dimensionless electron-electron interaction strength and manifesting clear signatures of enhanced Mott gaps at discrete fillings. An important nonperturbative finding is a remarkable fine-tuning effect of the precise lattice commensuration, where slight variations in the relative lattice periods may lead to a suppression of the correlated insulating phase, in qualitative agreement with the observed fragility of the correlated insulating phase in twisted bilayer graphene. Our predictions, which should be directly verifiable in bichromatic optical lattices, establish that the competition between interaction and incommensuration is a key element of the physics of moire superlattices.

Automated summary

Inspired by twisted 2D bilayer moire systems, we studied Coulomb interacting systems under two unequal period 1D lattice potentials, leading to a 1D bichromatic moire superlattice with flattened band and enhanced Mott gaps. Fine-tuning lattice commensuration plays a key role in the appearance of correlated insulating phase.