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

Abstract

Inspired by the rich physics of twisted 2D bilayer moiré 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 `moiré' 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 moiré superlattices.

arXiv comment7 pages, 9 figures

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Cited by in corpus (16)

• Magic angles and correlations in twisted nodal superconductors
• Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
• Incommensurability enabled quasi-fractal order in 1D narrow-band moiré systems
• Short-range interactions are irrelevant at the quasiperiodic-driven Luttinger Liquid to Anderson Glass transition
• Josephson effects in twisted nodal superconductors
• Reentrant topological phases and spin density wave induced by 1D moiré potentials
• Reentrant topological phases and entanglement scalings in moiré-modulated extended Su-Schrieffer-Heeger Model
• Topological states constructed by two different trivial quantum wires
• Interaction-induced reentrance of Bose glass and quench dynamics of Bose gases in twisted bilayer and quasicrystal optical lattices
• Quasiperiodicity-induced enhancement of superconductivity in one-dimensional critical systems
• Moiré Superradiance in Cavity Quantum Electrodynamics with Quantum Atom Gas
• Mobility edges and fractal states in quasiperiodic Gross-Pitaevskii chains
• Nonstandard Hubbard model and electron pairing
• Many-body tunneling in a double-well potential
• Effective Luttinger parameter and Kane-Fisher effect in quasiperiodic systems
• Fractal Quasicondensation in One Dimension