Hierarchical Relaxation in Large-twist-angle Moire Drives Supermoire Formation

Abstract

Supermoire lattices in large-angle twisted bilayers have recently been shown to emerge from periodic arrangements of commensurate stacking motifs, yet the microscopic structural mechanism governing their formation has remained unresolved. Here, we uncover the microscopic origin of supermoire order as a hierarchical lattice relaxation process. Combining force-field simulations with experimental validation via super-resolution, layer-resolved multislice electron ptychography, our results identify interlayer Se-Se repulsion at the picometer scale as the driving force, giving rise to coupled short-range (about 1 nm) moire relaxation and coexisting long-range (about 10 nm) supermoire modulation. These findings demonstrate that even picometer-scale lattice relaxation remains critical in large-angle moire systems and must be explicitly considered in understanding their emergent electronic and quantum phenomena.