A Self-Consistent Phase Field Crystal Method for Twisted Bilayer Graphene

Correlated electronic phenomena in magic-angle twisted bilayer graphene have garnered widespread research interest in two-dimensional materials science. As a powerful multiscale framework bridging atomic-scale resolution and mesoscopic structural evolution, the structural phase field crystal method has been widely adopted for graphene system studies. In this work, we develop a self-consistent XPFC model specifically for twisted bilayer graphene (tBLG) simulations. By globally optimizing the core free-energy functional parameters via a genetic algorithm, the proposed model achieves a marked improvement in consistency between the equilibrium density field and the first-principles generalized stacking fault energy surface. We further introduce a self-consistent dynamic interlayer interaction potential to replace the conventional fixed-substrate approximation, which captures the bidirectional coupling and mutual relaxation between adjacent graphene layers in a self-consistent manner. We calibrate the precise magnitude of the interlayer potential using the widths of stacking domain boundaries between distinct stacking configurations as a key metric, with the results benchmarked against atomistic simulation data. When applied to the 1.1° magic-angle tBLG system, the model uncovers spontaneous structural relaxation driven by interlayer van der Waals interactions: low-energy AB–BA stacking domains expand significantly, while high-energy AA domains shrink correspondingly.