Signatures of Flexoelectric Polar Vortex Superstructure and Electronic-Correlation-Modulated Screening in a Double-Moiré System

Nanoscale polar structures are essential for understanding polarization processes in low-dimensional systems and offer exciting prospects for high-performance electronics. Here, we reveal the signatures of a flexoelectric polar vortex superstructure in twisted bilayer graphene aligned with hexagonal boron nitride (TBG/hBN), where strong coupling between two moiré patterns induces pronounced structural relaxation. Scanning tunneling microscopy uncovers moiré-scale flat-band bending, distinct from domain-wall-confined polarization in minimally twisted graphene. Theoretical simulations demonstrate that the lowering of point-group symmetry plays a crucial role and indicate that the in-plane polarization field forms an array of polar vortices. Moreover, near the magic angle, the polarization becomes highly gate-tunable and couples to electron correlations, leading to spatially modulated correlated gaps. Our findings establish the coupling of multiple moiré patterns as a powerful strategy for engineering nanoscale polar structures and emergent quantum states.