Strain fields in twisted bilayer graphene

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long-wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity and localized structural deformations that introduce disorder and strain. In this study we used Bragg interferometry to capture atomic displacement fields in twisted bilayer graphene with twist angles <2°. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain were statistically evaluated, revealing the prevalence of short-range disorder in moiré heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anisotropically in saddle-point regions, generating distinctive striped strain phases. Our results establish the reconstruction mechanics underpinning the twist-angle-dependent electronic behaviour of twisted bilayer graphene and provide a framework for directly visualizing structural relaxation, disorder and strain in moiré materials. Complete strain tensor fields of twisted bilayer graphene are quantitatively mapped, revealing two-regime reconstruction mechanics depending on twist angle.