Composite solitons and their dynamics of two-component Bose–Einstein condensates in Moiré lattices

To address the inherent instability and symmetry breaking of dipole solitons in conventional periodic potentials, this study introduces a dual-component coupling mechanism within two-dimensional (2D) Moiré optical lattices to construct two types of composite solitons: fundamental-dipole solitons (FDS) and dipole-vortex solitons (DVS). By systematically investigating the bandgap structures and nonlinear dynamics under Pythagorean twist angles, it confirms that dipole solitons can achieve dynamic stability within specific parameter regimes due to the synergistic effects of Moiré flat bands and cross-phase modulation (XPM). Numerical simulations reveal distinct stabilization mechanisms for the two composite modes: the FDS utilizes the dynamically tunable effective potential generated by the fundamental soliton to counteract repulsive forces, whereas the DVS leverages the robust annular geometric barrier of the vortex soliton to physically trap the dipole soliton. Furthermore, we demonstrate that soliton destabilization under strong repulsion is fundamentally driven by profound internal density redistribution and spatial structural reorganization. These results elucidate the localization mechanisms of composite modes in Moiré geometries, providing a solid foundation for the manipulation of multi-topological-charge matter waves in ultracold atoms.