Moir\'{e} versus Mott: Incommensuration and Interaction in One-Dimensional Bichromatic Lattices

TL;DR

This paper investigates how incommensurate 1D bichromatic lattices influence electron interactions, revealing enhanced Mott gaps and a sensitive dependence on lattice commensuration, with implications for moiré superlattice physics.

Contribution

It introduces a non-perturbative analysis of Coulomb interactions in 1D bichromatic lattices, highlighting the impact of lattice commensuration on correlated insulating phases.

Findings

Enhanced Mott gaps at discrete fillings due to flattened bands.

Fragility of correlated insulators with slight lattice period variations.

Predictions applicable to bichromatic optical lattice experiments.

Abstract

Inspired by the rich physics of twisted 2D bilayer moir\'{e} systems, we study Coulomb interacting systems subjected to two overlapping finite 1D lattice potentials of unequal periods through exact numerical diagonalization. Unmatching underlying lattice periods lead to a 1D bichromatic `moir\'{e}' 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 non-perturbative 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 moir\'{e} superlattices.