Nonlinearity-induced dynamical self-organized twisted-bilayer lattices in Bose-Einstein condensates

TL;DR

This paper proposes a novel method to generate self-organized twisted-bilayer lattices in Bose-Einstein condensates using nonlinear atomic interactions, leading to dynamic moiré structures and flat-band phenomena, with potential for experimental realization.

Contribution

It introduces a new scheme to create dynamical twisted-bilayer lattices in BECs driven by nonlinearity, differing from traditional static approaches.

Findings

Nonlinear interactions induce both periodic and aperiodic moiré structures.

Dynamically generated flat-band physics observed in BEC wave packet dynamics.

Proposal feasible with current experimental techniques.

Abstract

Creating crystal bilayers twisted with respect to each other would lead to large periodic supercell structures, which can support a wide range of novel electron correlated phenomena, where the full understanding is still under debate. Here, we propose a new scheme to realize a nonlinearity-induced dynamical self-organized twisted-bilayer lattice in an atomic Bose-Einstein condensate (BEC). The key idea here is to utilize the nonlinear effect from the intrinsic atomic interactions to couple different layers and induce a dynamical self-organized supercell structure, dramatically distinct from the conventional wisdom to achieve the static twisted-bilayer lattices. To illustrate that, we study the dynamics of a two-component BEC and show that the nonlinear interaction effect naturally emerged in the Gross-Pitaevskii equation of interacting bosonic ultracold atoms can dynamically induce both periodic (commensurable) and aperiodic (incommensurable) moir\'{e} structures. One of the interesting moir\'{e} phenomena, i.e., the flat-band physics, is shown through investigating the dynamics of the wave packet of BEC. Our proposal can be implemented using available state-of-the-art experimental techniques and reveal a profound connection between the nonlinearity and twistronics in cold atom quantum simulators.